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EFFECTS OF PERTURBATIONS ON THE REVERBERANT SOUND FIELD OF A

ROOM

A Thesis in

Acoustics

Sumeet Sanjay Gawali

Submitted in Partial Fulfillment of the Requirements for the Degree of

Master of Science

May 2020 ii The thesis of Sumeet Gawali was reviewed and approved by the following:

Stephen Thompson Research Professor Thesis Advisor

Daniel Russell Teaching Professor of Acoustics and Distance Education Coordinator

Robert Smith Assistant Research Professor

Victor Sparrow Director of Graduate Program in Acoustics and United Technologies Corporation Professor of Acoustics

iii ABSTRACT

The reverberant sound field in a room, with all surfaces of the room being stationary, depends on the objects present in the room and their reflective or absorptive features and partly expressed in the reverberation time of the room. However, if perturbations are introduced in the sound field, either by moving objects in a room or by introducing new moving objects in the room with reflective or absorptive characteristics, the reverberant sound field undergoes modifications as the reflections change and in turn change how sound waves in a room interfere with each other at different locations in the room. These changes can be observed by making a comparison measurement between the frequency response of the room when it is stationary and when it is being perturbed. In this research effort, the impact on the time averaged sound field of a person moving through four candidate rooms was examined to assess the impact of this type of practical and easily achieved level of perturbation on a room. Hence, a comparison measurement was conducted in various rooms on the University Park campus of the Penn State University to analyze and study the effects of this type of perturbations on the sound field of a room. In the four types of rooms examined in this study, it was found that a person walking around did not produce what would be a significant improvement on averaging sound pressure level uniformity over the distribution of measured points in the rooms.

iv TABLE OF CONTENTS

LIST OF FIGURES ...... vi

LIST OF TABLES ...... x

ACKNOWLEDGEMENTS ...... xi

Chapter 1 Introduction ...... 1

Chapter 2 Reverberant and Diffuse field ...... 6

Reverberant field ...... 7 Diffuse Field ...... 9 Schroeder frequency ...... 10

Chapter 3 Overview of Measurements ...... 15

General Setup ...... 15 Equipment ...... 16 Audio Signal ...... 17 Sound Source ...... 17 Microphones ...... 19 Audio Interface ...... 19 Storage and processing ...... 20

Chapter 4 Measurements and Data Analysis ...... 22

Microphone sensitivity measurements ...... 23 Reverberation time (RT60) measurement...... 24 Background noise measurement...... 27 Comparison measurement...... 28 Stationary measurement ...... 28 Perturbed measurement ...... 28 Data Analysis ...... 29 Reverberation time (RT60) measurement ...... 29 Comparison measurements...... 31

Chapter 5 Conference Room – Data Analysis ...... 33

General construction and features ...... 33 Reverberation time (RT60) measurement...... 34 Preliminary calculations ...... 36 Background noise measurement...... 37 Comparison measurement...... 38

Chapter 6 Room #22 (Hammond Building) – Data Analysis ...... 44

v General construction and features ...... 44 Reverberation time (RT60) measurement...... 45 Preliminary calculations ...... 47 Background noise measurement...... 48 Comparison measurement...... 50

Chapter 7 Reverberation chamber – Data analysis ...... 56

General construction and features ...... 56 Reverberation time (RT60) measurement...... 57 Preliminary calculations ...... 58 Background noise measurement...... 59 Comparison measurement...... 61

Chapter 8 Ensemble A 132 (Music Building - II) – Data analysis ...... 68

General construction and features ...... 68 Reverberation time (RT60) measurement...... 69 Preliminary calculations ...... 71 Background noise measurement...... 72 Comparison measurement...... 73

Chapter 9 Conclusion ...... 80

Appendix Schroeder frequency ...... 83

LIST OF FIGURES

Figure 1-1: Experimental study conducted by Arthur Benade in his Laboratory space showing the effect of a person walking around in a room ...... 12

Figure 1-2 The four rooms measured for this research study ...... 5

Figure 2-1: Newell’s graph representing the concept of critical distance in a room...... 8

Figure 2-2: General categories of Room Modes...... 12

Figure 2-3: Frequency response of a rectangular room of volume 180 cu. m. showing the modal density of the room ...... 112

Figure 3-1: General signal flow chain...... 16

Figure 3-2: JBL Flip 4...... 18

Figure 3-3: Dayton Audio Emm6 Electret microphone...... 19

Figure 3-4: Zoom F8n Multitrack field recorder...... 20

Figure 4-1: B&K Type 4231 Sound Calibrator...... 24

Figure 4-2: Long’s graphical representation of the reverberation times for rooms varying in volume and purpose...... 25

Figure 4-3: Calculating the reverberation time using the impulse response of a room...... 26

Figure 4-4: Calculating the reverberation time using a steady sound source...... 26

Figure 4-5: Reverberation time calculation of the conference room...... 30

Figure 5-1: General charaterics and construction of Conference room...... 33

Figure 5-2: Ceiling and front of the Conference room...... 34

Figure 5-3: Reverberation time decay curve of Conference room...... 35

Figure 5-4: Spectral density of the background noise of the conference room...... 127

Figure 5-5: The individual spatial points and the Averaged spectral density for the 8 spatial points measured in the stationary condition...... 128

vii Figure 5-6: The individual spatial points and the Averaged spectral density for the 8 spatial points measured in the perturbed condition...... 128

Figure 5-7: Average spectral densities compared against each other in the frequency range from 200 Hz to 2000 Hz...... 39

Figure 5-8: Zoomed in response of the stationary and the perturbed conditions plotted together ...... 40

Figure 5-9: Zoomed in frequency response of the stationary and perturbed measurements from 1860 Hz to 1940 Hz ...... 41

Figure 5-10: Calculated standard deviation plotted along with the average spectral density .. 42

Figure 5-11: The calculated difference between the two standard deviation curves ...... 42

Figure 6-1: Room #22 in Hammond building ...... 45

Figure 6-2: Microphones set up in room #22…...... 45

Figure 6-3: Reverberation time decay curve of room #22...... 46

Figure 6-4: Spectral density of Background noise spectral density of room #22...... 49

Figure 6-5: Zoomed in background noise spectral density of room #22...... 49

Figure 6-6: Average spectral density versus individual spectral densities measured in the stationary condition...... 50

Figure 6-7: Average spectral density versus individual spectral densities measured in the perturbed condition...... 50

Figure 6-8: Average spectral densities compared against each other in the frequency range from 300 Hz to 2000 Hz...... 51

Figure 6-9: Zoomed in response of the stationary and the perturbed conditions plotted together...... 52

Figure 6-10: Zoomed in frequency response of the stationary and perturbed measurements from 1860 Hz to 1940 Hz ...... 53

Figure 6-11: Calculated standard deviation plotted along with the average spectral density .. 54

Figure 6-12: The calculated difference between the two standard deviation curves ...... 54

Figure 7-1: General characterisitics and construction of Reverberation chamber ...... 56

Figure 7-2: Reverberation time decay curve of Reverberation chamber...... 58

viii Figure 7-3: Background noise spectral density of Reverberation chamber ...... 60

Figure 7-4: Zoomed in background noise spectral density...... 61

Figure 7-5: Average spectral density versus individual spectral densities measured in the stationary condition...... 62

Figure 7-6: Average spectral density versus individual spectral densities measured in the perturbed condition...... 62

Figure 7-7: Average spectral densities compared against each other in the frequency range from 200 Hz to 2000 Hz...... 63

Figure 7-8: Zoomed in response of the stationary and the perturbed conditions plotted together ...... 64

Figure 7-9: Zoomed in frequency response of the stationary and perturbed measurements from 1945 Hz to 1993 Hz ...... 65

Figure 7-10: Calculated standard deviation plotted along with the average spectral density .. 66

Figure 7-11: The calculated difference between the two standard deviation curves ...... 66

Figure 8-1: Acoustic treatments on the ceiling and walls of Ensemble 132 (Music – Building II) ...... 68

Figure 8-2: Reverberation time decay curve of room Ensemble A 132...... 70

Figure 8-3: Background noise spectral density of room ensemble A 132...... 72

Figure 8-4: Zoomed in Background noise spectral density above 10 KHz of room ensemble A 132...... 73

Figure 8-5: Average spectral density versus individual spectral densities measured in the stationary condition...... 74

Figure 8-6: Average spectral density versus individual spectral densities measured in the perturbed condition...... 74

Figure 8-7: Average spectral densities compared against each other in the frequency range from 200 Hz to 2000 Hz...... 75

Figure 8-8: Zoomed in response of the stationary and the perturbed conditions plotted together...... 76

Figure 8-9: Zoomed in frequency response of the stationary and perturbed measurements from 1810 Hz to 1860 Hz...... 77

Figure 8-10: Calculated standard deviation plotted along with the average spectral density .. 78

ix Figure 8-11: The calculated difference between the two standard deviation curves ...... 78

Figure A-1: Frequency response of a rectangular room of volume 180 meters cubed showing modal density in the frequency range of 20 Hz to 315 Hz ...... 83

LIST OF TABLES

Table 1-1: Selected rooms and their physical and acoustical features...... 4

Table 2-1: Modes for the rectangular room having volume 180 cu.m...... 11

ACKNOWLEDGEMENTS

I would like to acknowledge the tremendous support and guidance provided to me by my advisor Dr. Stephen Thompson and his unconditional mentoring throughout my time being a graduate student in the department of Acoustics at Pennsylvania State University. I would also like to express gratitude towards the Program Director Dr. Victor Sparrow for his guidance since the very beginning and through important transitions.

I also express my heartfelt gratitude towards my committee professors, Dr. Daniel

Russell and Dr. Robert Smith for their timely help and guidance even through busy schedules. I would also like to thank Dr. Thomas Gabrielson and Dr. Michelle Vigeant and other professors who helped me push through roadblocks and keep pressing on towards the completion of my research here at Penn State.

I also extend my gratitude towards some of my peers who helped me with their precious knowledge and inputs and were the first responders towards the difficulties that came my way. I would like to thank Dr. Matthew Neal, Lane Miller and Cameron McCormick for their valuable guidance in times of need. Last but not the least, I would like to thank Aash Chaudhary and

Adwait Ambaskar for all their help.

I am also grateful towards Erin Ammerman and Melissa Wandrisco for helping me through all kinds of formalities and letting me check out things as and when required. Lastly, I would like to thank all the faculty in the department of Acoustics who have helped me in one way or the other and without whom, completing this research and thesis would not have been possible.

Chapter 1

Introduction

This study is motivated by a previous study done by Lane Miller [1] who attempted to measure the amplitude of sound in the reverberation chamber. The main objective of Miller’s study was to check the effectiveness of an array of loudspeakers, embedded in the frame of a window, to cancel incoming noise. The concept behind this earlier study was based on noise cancellation. The incoming noise, after being detected and fed into the system, gets reversed in phase and this new signal is fed through the speaker in order to get zero net noise into the enclosure.

While testing this array of loudspeakers, the strong room modes present in the reverberation chamber interfered with the study. The array of loudspeakers was tested by projecting sinusoidal pulses of single frequency at different angles, and their ability to cancel noise was studied. The sinusoidal pulses used for testing were in the frequency range of 250 Hz to a 1000 Hz. With this in mind, the analysis of the measurements done in this study was limited up to 2000 Hz.

Under steady conditions, an enclosure or a room has a specific behavior - frequency response - to different excitation frequencies. This frequency response is one of a kind for different spatial positions in the room. Reflected waves from walls or other objects in the room that arrive at a point interfere constructively or destructively depending on the phase of the reflected waves and this interference changes at other points. If objects are displaced, or even moved around in a room, the reflections are altered and in turn the frequency response at particular locations in the room as compared to the original frequency response changes.

2 The main theory behind this study is motivated by a statement from Benade [2] where he states:

“1. for any frequency of excitation and source location, there are microphone

positions in a room at which the detected sound pressure is particularly

insensitive to the effects arising when objects are moved around in a room. There

is generally a strong transmission of sound to the microphone at such positions

and things are little changed if the frequency is altered slightly.

2. for any given excitation frequency and source location, there are a few

microphone positions in the room at which the sound pressure is extremely low.

When objects are moved around in the room, there are enormous fluctuations in

the microphone signal. The positions in the room of such points of minimum

sound pressure and wild signal fluctuation are considerably displaced if a small

change is made in the excitation frequency.”

Benade set up an experiment to study these phenomena in his laboratory space where he had a corner mounted source running at a frequency near 600 Hz. Figure 1-1 a shows what the microphone response signal looked like when Benade walked slowly around the laboratory room and back to the point where he started walking from. According to Benade the graph showed a certain amount of fluctuation in the microphone signal as his body altered the arrangement of the characteristic patterns of the room modes. In the middle portion of the graph, his perambulations took him into a region that had a particularly large influence. Also, the pressure signal was the same after his return to the starting point as it had been originally.

In the second part of his experiment, the source location and the point of departure for

Benade’s room circumnavigation remained unchanged. The chief alteration was a small change in the excitation frequency, about 5 or 10 Hz. The new frequency was critically chosen to give a

3 small response at the microphone position. Figure 1-1 b shows that the recorded trace made under these conditions show enormously large and complex fluctuations in the microphone signal.

Figure 1-1: Experimental study conducted by Arthur Benade in his Laboratory space showing the effect of a person walking around in a room. a) upper trace – the fairly uniform transmission observed at a selected frequency for which the for which the transmission to the microphone is particularly strong b) lower trace – the much wilder fluctuations observed for a nearby frequency that produces particularly small transmission to the same microphone position. (from [2] Figure

11.4)

4 Arthur Benade was the Ph. D advisor for my current research advisor Dr. Stephen

Thompson. In a private conversation with Dr. Thompson, Benade said that taking measurements at multiple spatial positions while perturbing the room with a moving object such as a person walking slowly in the room and averaging the measurements would improve the measurements made in any room. However, Benade did not set up a laboratory experiment to study this theory.

Dr. Thompson was the research advisor for Lane Miller [1] and hence wanted to explore ways to improve the measurements attempted by Miller in his study. To understand whether the perturbations introduced in a room improved the measurements being taken, a comparative study was set up and analyzed in 4 rooms on the University Park campus of the Pennsylvania State

University. The rooms chosen were distinct from each other in terms of general construction, size and reverberation times. Table 1-1 shows the features of the rooms studied and includes features that were measured as well as calculated in the course of this study.

Reverberation Critical distance No. of Spatial Rooms Volume (푚3) time (푅푇60) (sec) (푓푡) points

Reverberation 117.25 4.06 1.41 4 Chamber

Conference room 95.73 0.712 3.74 8

Room #22

(Hammond 773.05 1.37 6.3 20

Building)

Ensemble A 132 1126.03 1.68 6.87 30

Table 1-1: Selected rooms and their physical and acoustical features.

5 The calculations and measurements for all the features listed in the table for all the rooms will be discussed in detail in the following chapters. Figure 1-2 shows the 4 rooms chosen for this study.

Figure 1-2: The four rooms measured for this research study: from top left in clockwise direction. a. Conference room (Applied Science Building 2nd floor) b. Room #22 (Hammond Building) c. Reverberation chamber (Hammond building) d. Ensemble A 132 (Music Building – I)

Chapter 2

Reverberant and Diffuse field

In free space, the amplitude of sound radiated by a loudspeaker falls off with distance from the speaker due to spherical spreading. In a room, the sound reflects from the walls and other objects in the room to provide the reverberant field, which is no longer characterized by simple spherical spreading, in places remote from the source. Very near the source, the direct radiated field from the speaker dominates the reverberant field. Very far from the source, the reverberant field dominates. Thus, the presence of a sound source in an enclosure, gives rise to two types of sound fields – direct and reverberant. Simply put, if an observer is close enough to the source, the sound that is heard can be considered to be the direct sound from the source. On the other hand, if the observer is far away from the source, the sound heard is dominated by the reflections in the room and is a result of the net reflected sound waves. This sound field, sufficiently distant from the sound source, is known as the reverberant field. The direct field depends solely on the sound source. However, the reverberant field depends on the characteristics of the enclosure and may sometimes also depend on the objects present in the enclosure.

In contrast to the reverberant field, an enclosure with very few or no reflections is known to be a non-reverberant field. This absence of reflections may be due to presence of absorbing surfaces on the periphery of the room or presence of objects that disperse the reflecting waves into different random directions so that they do not reach the observer but instead undergo numerous reflections and eventually lose energy in the form of heat and eventually decay completely.

7 Reverberant field

Heinrich Kutruff [3], states that in a room that is reverberant the sound produced in the room will not decay immediately after the sound source is cut off, but remains audible although with decreasing loudness. The process of sound decay in a room depends significantly on the structure of the sound field.

Marshall Long [4] states that near the source the direct-field contribution is larger than the reverberant field contribution and the fall off behavior is that of a point source in a free field.

In the far field, the direct-field contribution falls below the reverberant-field energy and the sound pressure level is constant throughout the space. Long [4] defines critical distance as the distance where the direct-field level equals the reverberant-field level.

Phillip Newell [5], explains critical distance. Figure 2-1 represents the graphical concept of critical distance of a room. The sound level decreases as a listener moves away from the source. Beyond the critical distance, it becomes constant and does not change which is true in the conceptual limit of a perfectly diffuse field. This can be measured by a sound level meter, which can further be used to measure the critical distance in a room, by placing a sound source exciting the room with a constant sound power and measuring the sound pressure level with a sound level meter, close to the sound source preferably on axis of the sound source if it is not omnidirectional. When the observer starts moving away from the source the sound pressure level indicated by the meter will show a decrease in sound pressure level. At a certain point the sound level stops changing and becomes constant even if the observer keeps moving further. The distance at which the sound pressure level indicated by the sound level meter stops falling further and becomes constant is the critical distance of that room.

Figure 2-1: Newell’s graph representing the concept of critical distance in a room. The x-axis represents the logarithmic distance from the sound source and the y-axis represents the Sound pressure level. (from [5] Figure 11.21)

The critical distance is affected by characteristic features of a sound source and the enclosure in which the sound source is placed. The critical distance pertaining to any set of sound source and enclosure is given by the formula [6]

1 훾∗퐴 푑 = √ (2.1) 푐 4 휋

where

푑푐: critical distance in meters

훾: degree of directivity

A: Absorption of the room (푚2)

The formula for critical distance is further approximated using Sabine’s formula (Long [4] eq.

8.59) for reverberation time.

0.161×푉 푅푇 = (2.2) 60 퐴

where

푅푇60: Reverberation time of a room in seconds

V: Volume of the room in 푚3

Using Sabine’s formula, the equation for critical distance yields,

훾×푉 푑푐 = 0.057√ (2.3) 푅푇60

Equation 2.3 was used throughout this research and thesis to calculate the critical distance for the

4 rooms measured.

Directivity

Long [4] explains the concept of directionality, directivity and directivity index with regard to a sound source. He elaborates that for many sources, the sound pressure level at a given distance from the center is not the same in all directions. This property is called directionality and the changes in level with direction of a source are called its directivity. The sound power level of a source gives no specific information about the directionality of the source. A highly directional source could have the same sound power level as an omnidirectional source but would produce a very different sound field. The difference is accounted for by defining a directivity index, which is the difference in decibels between the sound pressure level from an omnidirectional source and the measured sound pressure level in a given direction from the real source.

Diffuse Field

A diffuse field is possible in reverberant fields only. In other words, all diffuse fields are reverberant but not all reverberant fields are diffuse. Kutruff [3] explains diffuse field as a field in which the sound energy density is same regardless of the spatial position and at any particular spatial point, and the sound arriving from all directions is equal.

10 Kutruff goes on to say that a real sound field can never be completely diffuse as there will be no net energy flow within the room. A diffuse sound field is difficult to achieve in rooms where the walls have the tendency to project the reflected sound energy in specific directions. A room that consists of acoustically rough walls helps to attain the diffuse condition better than smooth ones as the irregularities scatter the incident sound energy in a wide range of directions.

However, any wall or ceiling will diffuse only a certain fraction of the incident sound and the remaining part is reflected in specific directions.

Furthermore, the tendency of the room surface reflections to contribute towards achieving a diffuse field condition is also limited by the absorptivity of the boundary and the irregular spatial distribution of absorption. A typical situation is that of an occupied hall. In a concert hall most of the absorption is affected by the audience which is usually present on the floor of the hall.

The absorptive portions of the boundary reduce potential ray paths and hence obstruct the formation of a diffuse sound field.

Schroeder frequency

Long [4], explains the sound in rooms in great detail. He says that the analysis of sound in a room falls into regions according to the frequency (wavelength) of the sound under consideration. At low frequencies, where the wavelength is greater than twice the length of the longest dimension of the room, only plane waves can be formed and the room behaves like a duct. This condition can occur in very small rooms. Above the cut off frequency of a room, normal modes are formed, which are manifest standing waves having localized regions of high and low pressure. At still higher frequencies the density of modes is so great that there is a virtual continuum in each frequency range and it becomes more useful to model room behavior based on the energy density or other statistical considerations.

11 Long goes on to describe the normal modes in rectangular rooms. He adds that when a room is excited using a sound source and then the sound source is removed, certain frequencies persist. However, modes may develop in several directions if there is no room dimension that is small compared with a wavelength. Long derives the equation for natural frequencies (Eq. 2.4) by applying the three-dimensional wave equation in rectangular coordinates and writing a general equation.

The natural frequencies are given by,

2 2 2 푐0 푙 푚 푛 푓푙푚푛 = √( ) + ( ) + ( ) (2.4) 2 푙푥 푙푦 푙푧

where, 푙푥, 푙푦, 푙푧 are the dimensions of the rectangular room and 푙, 푚, 푛 are integers that indicate the number of nodal planes perpendicular to the x, y and z axes, and 푐0 is the speed of sound in air.

The normal modes of a rectangular room are referenced by whole number indices represented by three letters 푙, 푚 and 푛. For example, the (1,0,0) mode would be the fundamental mode in the x direction and (2,1,0) mode is a mode in the x and y direction.

For example, consider a rectangular room having dimensions 15x12x10 meters. Using equation 2.4 for calculating the various modes and their natural frequencies, we get the values listed in Table 2-1.

Mode Natural frequency (Hz) Mode Natural frequency (Hz)

(1,0,0) 11 (2,0,0) 22

(1,1,0) 18 (2,1,0) 27

(1,1,1) 25 (2,1,1) 32

Table 2-1: Modes for the rectangular room having dimensions 15x12x10 meters and their natural frequencies.

12 The frequency at which this rectangular room will be driven will determine which mode gets excited. For example, if the room is driven at a frequency of 11 Hz only 1 mode will get excited as evident from Table 2-1. If the room is driven at a frequency of 32 Hz, (2,1,1) mode will get excited. On the other hand, if the room is excited by a narrow band noise source from 0-

32 Hz, all 6 modes listed in Table 2-1 will get excited in the sound field of the room. The natural frequencies of the modes will depend on the dimensions of the room. The dimensions for rectangular rooms vary across the 3 axes. However, the fact that the number of modes excited by a sound source increases with an increase in the range of the driving frequency, remains true for all rooms which are neither perfectly absorptive nor perfectly reflective.

Room modes are generally categorized into 3 types – axial, tangential and oblique. Figure

2-2 shows the three types of room modes possible in a rectangular room. Everest and Pohlmann

[7], explain these categories further. The axial modes correspond to waves which move parallel to

1 axis of the room. They are (푛푥, 0,0), (0, 푛푦,0) and (0,0, 푛푧) modes. Axial modes make most prominent contribution to acoustical characteristics of a room. Tangential modes correspond to waves which move parallel to a pair of room surfaces. They are (푛푥, 푛푦,0), (0, 푛푦, 푛푧) and

(푛푥,0, 푛푧) modes. Tangential modes have only half the energy of axial modes but their effect on room acoustics can be significant. Oblique modes bounce off all 3 room surfaces and are

th (푛푥, 푛푦, 푛푧) modes. Oblique modes have 1/4 energy of the axial modes.

Figure 2-2: General categories of Room Modes room modes as illustrated by Everest and

Pohlmann. (from [7] Figure 13-5)

13 Figure 2-3 shows the frequency response of a rectangular room. The volume of the room measured was 180 cubic meters. The figure represents the modal density of the room in the frequency range of 20 Hz to 315 Hz.

Figure 2-3: Frequency response of a rectangular room of volume 180 cu. m. showing the modal density of the room. (from [9] Figure 6.2)

In the low frequency range, the modal density is considerably low which means that different modes getting excited in this range can be identified and detected experimentally.

Looking further and going into higher frequency ranges, the modal density becomes so high that the different modes getting excited in this range can neither be identified separately nor detected experimentally.

The frequency beyond which the modes can no longer be individually detected is known as the Schroeder frequency. The Schroeder frequency for the room whose response is shown in

Figure 2-3 is around 80 Hz – as evidenced by the transition from room modes being dominant below 80 Hz to a more statistical response above 80 Hz.

Shroeder frequency of a room can be calculated using the formula (Long [4])

푅푇 푓 = 2000√ 60 Hz (2.5) 푠 푉

where,

fs – Schroeder frequency in Hertz, 푅푇60 – Reverberation time of the room in seconds

V – Volume of the room in m3

14 It is evident that the Schroeder frequency of any room depends on characteristics such as the volume of the room and the reverberation time of the room. As mentioned earlier, these characteristics can be very specific depending on the structure of the room and the geometry and the physical constitution of the room. Therefore, every room has its own specific Schroeder frequency.

Chapter 3

Overview of Measurements

General Setup

This research study was going to be applied for improving measurement of the array of noise cancelling loudspeakers that Miller [1] tried to study. Due the challenges that were involved in using the reverberation chamber, it became important to find alternate methods or enclosures where the array of loudspeakers could be effectively measured without the room’s behavior affecting the measurement.

Long [4] explains reverberation chambers briefly. He says separate hard-surfaced rooms serving as reverberation chambers can have characteristic resonant frequencies. A resonant device preferentially absorbs energy from the driving mechanism and returns it at a later time. During

Miller’s study, some of the frequencies of excitation that he used, seemed to emphasize this behavior of the existing reverberation chamber. Some harmonics due to these characteristic resonant frequencies existed longer, especially because of the reverberation time of the reverberation chamber being about 4 seconds.

In this study, the general method consisted of playing broadband noise signal through a sound source and recording the reverberant sound field with 4 microphones and at different spatial positions in the room. These recorded files were analyzed using different signal processing techniques which will be discussed in chapter 4 in detail. The frequency response was calculated and plotted to analyze the sound field recorded by these microphones.

16 Each measurement consisted of 4 different sub-measurements – background noise measurement, reverberation time measurement and the two conditional measurements: stationary and perturbed. All measurements will be discussed in detail in chapter 4.

Equipment

Different rooms were measured at different locations in the University Park Campus of the Pennsylvania State University and hence, portability was prioritized while selecting the equipment. The idea was to have the least amount of equipment required to effectively carry out measurements in every single room. The equipment selected, was based up on the signal chain that was drafted for the measurements. Figure 3-1 shows the signal flow chain which was the first thing to be conceptualized. The audio signal block symbolizes the test sound signal that was used to excite the room. The reverberant sound field was captured in different spatial positions by 4 microphones placed beyond the critical distance of the room. This recorded audio signal was transferred into a storage and processing device through an audio interface.

Figure 3-1: General signal flow chain used throughout the research study. All the measurements conducted followed this exact signal flow chain.

17 Audio Signal

The audio signal used for measurements was broadband noise. According to Long [4] the most commonly encountered audio signals for measurements are pink noise or white noise. He states that pink noise has equal energy per octave or a third octave. White noise has equal energy across all the frequencies. The power of pink noise decreases as 3 dB per octave with an increase in frequency. The white and pink noise signals used for the measurements were created using

MATLAB software and used throughout the research study. These test signals were created at a sampling frequency of 44.1 KHz and had a duration of 30 seconds each.

Sound Source

The sound sources used for exciting a room in the field of architectural acoustics require a system that shows a good frequency response and one that can produce high sound power. Such systems are usually used to measure the sound transmission loss between rooms across partitions and are bulky and draw a lot of power from a driving amplifier and do not fall under the category of portable systems. The measurements to be conducted in this study only required the excitation of sound field in a room. Also, the sound source needed to be portable enough with a good frequency response because the sound source was to be used in different locations on the Penn

State campus. That is where the JBL Flip 4 wireless speaker became an interesting yet effective solution. Figure 3-2 shows the physical structure of the speaker.

The specifications sheet provided by the manufacturer, indicates operating frequency range to be from 70 Hz to 20 KHz and the dimensions of this speaker are 2.67x6.88x2.75 inches making it portable. The Bluetooth connectivity option gives extra flexibility while using it along with any device that supports Bluetooth.

Figure 3-2: JBL Flip 4 – the portable speaker used as a sound source for measurements.

When this speaker is positioned as shown in the figure, the two active drivers point directly towards the listener and make it slightly directional. Crocker [9] states that when a point source, which would normally create spherical wavefronts of sound, is placed on a perfectly reflecting flat plane, the radiation from the source is restricted to a hemisphere. In practical applications, when drivers are placed in enclosures, similar phenomenon takes place. However, since the enclosures are never perfectly reflecting, the drivers radiate sound behind the enclosure as well but not as much as in the direction in front of the enclosure. This gives rise to a cardioid directivity pattern and the degree of directivity for cardioid patterns is around [10]. The degree of directivity increases as the source becomes more directional.

Considering the frequency range of interest for this study that is 200 Hz to 2000 Hz, in the lower frequency range, especially around 200 Hz, the wavelength turns out to be 1.7 meters and the half wavelength is 0.85 meters. At these low frequencies, the dimensions of the speaker driver become smaller than a quarter wavelength and the speaker radiates sound as an omnidirectional source. However, the degree of directionality for an omnidirectional source is unity. Therefore, even if the speaker radiates sound as an omnidirectional source at low frequencies, the usage of the degree of the directivity for the cardioid pattern in the formula for critical distance results in overestimation since, according to equation 2.3, the critical distance is directly related to the square root of the degree of directivity.

19 Microphones

Figure 3-3 shows the microphone selected for the measurements. Dayton audio EMM6 is an electret condenser measurement microphone which is easily available in the market at a very reasonable cost. It has a frequency response in the range of 18 Hz – 20 KHz covering the entire audible frequency range. The microphone weighs 144 grams and has a length of 7.5 inches which makes it very portable. A set of 4 EMM6 microphones was obtained to increase the number of spatial points recorded during a single measurement.

Figure 3-3: Dayton Audio Emm6 Electret Microphone was used to measure sound at different spatial points in a room.

Audio Interface

Portability was a deciding factor for all the equipment that was chosen for this measurement. The need for transferring equipment from one room to the other on campus called for a system that was light and portable enough to be carried to different parts of the campus by a single person.

Figure 3-4 shows the audio interface, Zoom F8N multitrack recorder, chosen for the measurements. It has 8 input channels with pre-amps and can operate up to a sampling frequency of 192 KHz. It can be operated on batteries when a power source isn’t readily available. The

20 zoom F8N can be used as a USB interface between the microphones and a digital audio workstation available on a computer. The recorder has about 512 GB of compatible storage in the form of external memory cards which enables it to function even in the absence of a computer.

The dimensions of the recorder are 7x2.1x5.5 inches which is considerably small compared to some other recorders with similar number of channels.

Figure 3-4: Zoom F8n Multitrack Field Recorder was used as an interface to record and save measurements on a computer.

Storage and processing

The recorder used throughout the measurements was capable of recording and saving files autonomously. However, for analysis and signal processing, the data stored on the recorder would have to be transferred to a computer which was being used for signal processing. To save the time needed for data transfer, the recorder was used as an audio interface and all the recorded files were stored directly on a computer. MATLAB was the primary software used for signal processing throughout this study. The frequency response for all the measurements was analyzed by calculating the spectral density of the recorded sound files. Time averaging for each second of the recorded data was an important step during analysis as it reduces the noise recorded in the measurements and also gives an overall change caused because of the perturbation. The frequency response was analyzed by setting 1 Hz as the resolution to extract important details.

21 Other software used were Audacity and Adobe audition to record and edit the recorded sound files. Data analysis will be explained in detail in chapter 4.

Chapter 4

Measurements and Data Analysis

The general procedure that was followed while measuring each room will be discussed in detail in this chapter. The different measurements and some general measurement procedures will be mentioned in these initial paragraphs before getting into the details of the same in the sections to follow.

To have the microphones effectively placed in the room’s reverberant field, the microphones were placed beyond a distance equal to the critical distance from the speaker. The wavelength for a sound signal at 200 Hz comes out to be 1.7 meters and consequently, the half wavelength for the largest wavelength in the frequency range of interest is calculated to be 0.85 meters or 2.79 feet. To provide independent samples of the sound field, the microphones were spaced at least one-half wavelength apart at the lowest frequency of interest.

The first step was to carry out preliminary calculations which included calculating the volume, reverberation time, critical distance and the Schroeder frequency of the room. For smaller rooms, the dimensions were measured by using a tape measure whereas for larger rooms, floor plans present in the database were used.

The measurements conducted were very straight forward and easy to execute, but some challenges had to be dealt with while handling each room. The values used to estimate the volume of a room were taken directly from the floor plan of the facility. Hence, the volume calculated in each measurement refers to the volume of the rooms without any object present in it.

Whereas in reality, presence of objects in a room decreases the volume.

Considering the formula used to calculate the critical distance in equation 2.3, the volume of a room is directly related to the critical distance, provided that the other parameters do not

23 change. If the volume decreases, the critical distance should also decrease. Having an excess value for volume will lead to an over estimated critical distance. Since, this distance is being used to estimate the distance beyond which the reverberant sound dominates the overall sound field in the room, having a bigger value will contribute towards enabling the measurements to be conducted deeper into the reverberant field than at the exact boundary at which the reverberant and direct sound energies are equal.

Sound isolation was another challenge during measurements. Each room measured was connected to other rooms by means of a corridor and the doors were not completely sealed in most cases. This made it easy for external noise to leak into the room during measurements. For example, someone turning on a piece of equipment or someone walking outside with a noisy pair of shoes or sometimes even people having a conversation in the corridors. Some of these happened while the room was being measured and added an extra variable to the study. In such incidents, a decision was made to discard the recording and to repeat the same measurement after the noise has stopped or decreased considerably compared to the sound source.

Another challenge associated with larger rooms, such as room #22 in Hammond building and room ensemble A132 Music Building – II, was the available space for measurement. In these rooms, the ceiling was higher than a regular room. The ceiling heights for both the rooms is over

20 feet while the microphone stands available for the measurements reached up to a height of 7 feet. This indicates that even after measuring several spatial points in the room, it was not possible to measure the sound field in the upper half of these rooms.

Microphone sensitivity measurements

Four microphones were used throughout this research study. All the microphones were of the same company and model and the microphones are said to have a similar frequency response

24 over the entire frequency range. The microphones were calibrated using a B&K type 4231 sound calibrator. Figure 4-1 shows the sound calibrator that was used to calibrate the microphones used in this study. This sound calibrator emits a 1 KHz tone at an amplitude of 94-dB.

Figure 4-1: B&K Type 4231 sound calibrator was used to calibrate microphones used for measurements.

The sound calibrator is made to calibrate 1 inch and ½ inch microphones (with a removable adapter). Whereas, the microphones used for this study were ¾ inch microphones. To have a tight seal around the microphone and the calibrator, a piece of paper was folded and fixed around the microphone leaving some distance from the tip. The microphones were calibrated with the calibrator with a frequency of 1000 Hz at 94 dB.

Reverberation time (푹푻ퟔퟎ) measurement

An important parameter required for the preliminary calculations was the reverberation time (푅푇60). The reverberation time of a room is defined by the time required for the excited sound field in a room to decay by 60 dB [4]. Figure 4-4 shows Long’s graphical representation of the reverberation times for rooms being used for various purposes and having different volumes.

Long goes on to state that these values have changed over time because of amplified sound

25 reinforcement of instruments, which has led to a decrease in these required reverberation times for spaces.

Figure 4-2: Long’s graphical representation of reverberation times for rooms varying in volume and purpose. (from [4] Figure 17.10)

The reverberation time of a room can be measured by using two methods. The first method includes having a simple impulse sound source to excite the room and then recording it with a microphone. Figure 4-3 shows this method graphically. This recorded sound file is then analyzed to calculate the reverberation time of the room. The second method to calculate reverberation time is to use a steady sound source to fill the sound field in the room until it achieves steady state and then turning the sound source off. Figure 4-4 represents this method graphically. The sound field in the room does not drop off instantly but takes some time to decay

26 even after the sound source is turned off. This decay can be measured and used to calculate the reverberation time of a room.

Figure 4-3: Reverberation time calculated using the response of a room to an impulse sound source.

Figure 4-4: Reverberation time calculated using a steady sound source and measuring the decay time after the sound source is cut off.

The first method, using an impulse as a source of exciting the room, was chosen to calculate the reverberation time of the four rooms that were measured. An impulse is a sudden burst or pop which has a very narrow-peaked shape in the time domain. The narrower the peak in the time domain, the wider is the response in the frequency domain. There are multiple impulse

27 sound sources that can be used to excite the room for this measurement. Impulse sound sources like a gunshot or a balloon pop are typically used while measuring the reverberation time of a room. A recorded gunshot has a narrower peak than the balloon pop. The selection of the impulse sound source depends on the frequency range of interest or the range of frequencies that need to be excited depending on the frequency range of interest. If you require to excite a wide range of frequencies, a gunshot can be used. On the contrary, if the frequency range of interest is up to

2000 Hz, a balloon pop or a simple clap can be used as an impulse sound source.

The presence of background noise in a room sets limitation on the reverberation time measurement by decreasing the dynamic range available for measuring the entire 60 dB sound decay, according to the definition of reverberation time. In cases like these, by analogy to 푅푇60,

푅푇20 or 푅푇30 can be defined as the time required for the sound pressure level (SPL) to drop by 20 dB or by 30 dB, respectively. The 푅푇20 and 푅푇30 times can be multiplied by a factor of 3 and 2 respectively to calculate the 푅푇60 reverberation time. Hence, while calculating the reverberation time of the rooms measured, 푅푇60 reverberation time was calculated by first calculating the 푅푇30 time and then multiplying it by a factor of 2. The reverberation time calculations and plots pertaining to each room, will be discussed and shown in further detail while discussing the measurements conducted in each room separately.

Background noise measurement

Background noise measurement was an important step to analyze the noise present in a room to ensure that a good signal to noise ratio is achieved in the frequency range of interest that is from 200 Hz to 2000 Hz. Each room measured was equipped with HVAC, water pipes and electrical systems including electrical panels and lighting fixtures. The rooms were connected to other rooms by means of corridors, which cause external noise leakage into the rooms. Under

28 such circumstances, it became important to analyze the background noise and monitor the noise floor during measurements.

Comparison measurement

As mentioned earlier, due to the low sound isolation, a close attention was paid towards the external noise sources. In the comparison measurement, various spatial positions were measured in a room. To ensure that the exact spatial point is being measured in the stationary as well as the perturbed condition, the measurements were conducted in an alternating order. After positioning microphones on the spatial points chosen, the stationary conditional measurement was followed by the perturbed conditional measurement. After measuring the spatial point for both the conditions, the microphones were displaced to the next set of spatial points.

Stationary measurement

The first part of the comparison measurement was to measure the room in a stationary condition. The stationary condition refers to the objects in the room including the equipment used for measuring the room and the person operating the equipment.

Perturbed measurement

The perturbed measurement was the second part of the comparison measurement. The perturbations were introduced in the room by a person walking around in the room at normal speed. It was ensured that the perturbations that were introduced were in the reverberant field and

29 not in the direct field of the sound source. This was ensured by the person always being at a distance greater than the calculated critical distance.

Data Analysis

Several spatial points were measured for the 4 rooms selected for the study, and hence the amount of data collected was also large, about 3 GB. The data analysis for all the 4 rooms was broken down into parts depending on the various measurements conducted in the rooms.

MATLAB software was primarily used for all the data analysis and signal processing. Other software used for recording and editing were Audacity and Adobe Audition.

Reverberation time (푹푻ퟔퟎ) measurement

Reverberation time was the first measurement to be done in the rooms. A simple physical clap was used as an impulse sound source to excite the room. In the time domain, the recorded signal ranges from a negative maximum amplitude to a positive maximum amplitude. The signal processing procedure used for analyzing the reverberation time recordings were put forth by

Gabrielson [8]. The sound recording of the impulse signal was filtered using an octave filter and then the filtered output was squared. This filtered and squared output was exponentially averaged to produce an envelope of the time-domain waveform and the output values were converted to deciBels using 1 wave-unit squared as a reference. This makes the calculation of the reverberation time easier as compared to the original time domain waveform of the impulse sound source. Figure 4-5 shows the reverberation time measurement of the conference room that was chosen for this study. The red line that represents the 30-dB decay of the sound field is just a line drawn between the two points on the curve where the sound pressure level drops by 30-dB.

Figure 4-5: Reverberation time of the conference room calculated from the response of the room to an impulse sound source.

The time taken by the sound to decay by 30 dB (푅푇30) can be calculated by subtracting the abscissa of first point from the abscissa of the second point. The first point refers to the point on the decay line that has a smaller value for its x-intercept while the second point refers to the point on the decay line that has a greater value for its x-intercept. By multiplying 푅푇30 by a factor of 2, the 푅푇60 reverberation time of the room was calculated.

In Figure 4-5, a closer observation to the sound pressure level axis shows a dynamic range of about 70-dB above the noise floor. In theory, it should be possible to be able to calculate the 푅푇60 reverberation time from the dynamic range achieved in the measurement. The practical challenge that arises in the calculation of reverberation time is the presence of coupled spaces.

When a room has an opening into a space outside the enclosure by means of a door or when the room is not completely isolated from the external spaces, the sound waves from the sound source travel into these external spaces and bring about modification in the linear decay of the sound. In

Figure 4-5, the slope of the decay curve changes before 1.6 seconds and after about 2 seconds.

31 Therefore, even after having a dynamic range of about 70-dB above the noise floor, the entire 60 dB decay time (푅푇60) cannot be calculated because of the presence of couple spaces with an enclosure. If the room was perfectly isolated from the external spaces, the decay curve of the room would have a linear decay with a constant slope where the calculation of the 푅푇60 reverberation time is possible if the dynamic range of sound in the sound field is more than 60- dB.

Comparison measurements

Two different conditions were measured at several spatial points in a room. Each of these measurements at each spatial point was analyzed using the exact same process throughout the study and across the 4 rooms. The test audio signal used for exciting the room and the sound file recorded by each microphone, had a duration of 30 seconds. A 1.0 second time-averaged Fast

Fourier Transform was calculated for each recording to give a resolution of 1 Hz in the frequency domain. After calculating FFT for all the spatial points of a particular room, they were spatially averaged by averaging the different spatial points into one average Fourier Transform in the frequency domain. Also, to further understand the difference between stationary and perturbed conditions, standard deviation for both the conditions were calculated and analyzed.

The volume of data recorded in this research study was about 3 GB and numerous spatial points were studied for each room. To be able to compare the rooms regarding their response to perturbations against its stationary condition, supplementary calculations, measurements and the results of the analyses will be documented by following a common pattern. The documentation will follow the order – general construction and features of the room, reverberation time measurement, preliminary calculations (critical distance and Schroeder frequency), background noise measurements and the comparison measurement (frequency response).

32 Presenting the stationary and perturbed measurements separately, will make it difficult to compare the two and analyze and point out the exact differences between them. To make the comparison easier, the frequency responses of both the measurements will be presented on a single plot. Having a 1 Hz resolution in the frequency range of 200 Hz to 2000 Hz amounts to about 1800 points in the graph that can be compared. In addition to that, more than 15 spatial points were measured in rooms with large volumes. Hence, to summarize the comparison and to avoid cluttering of graphs, peculiarities will be focused on during the presentation of results in this document.

Chapter 5

Conference Room – Data Analysis

General construction and features

The conference room is a small room suitable to accommodate fewer than a dozen people and meant for close proximity discussions or sometimes for presentations for a small group of people. It is designed in a way that the distance between the person that is speaking, and the listener is roughly 4 meters. Long [4] throws light on the requirements for different kinds of rooms used for special purposes. He explains the dynamics and the construction that a conference room should have to be acoustically appropriate.

Figure 5-1 and 5-2 show the general construction and features of the conference room.

The conference room is a small size conference room populated with furniture like a wooden table, chairs and some bookshelves fairly populated with books. The ceiling of the room is made up of ceiling panels exactly above the table. The floor is covered throughout with carpet.

Figure 5-1: The overall construction and characteristics of the conference room.

Figure 5-2: Ceiling and front wall construction of the conference room.

According to Long [4], strong reflections from the ceiling aid in cross-table conversations. For the people sitting around the table, the reflections from the surface of the table help in speech intelligibility and conversations and hence, looking at the ceiling construction, the area exactly above the table is made up of ceiling panels which seem absorbent. However, for the people seated away from the table along the perimeter of the room, the reflections from the table might not be as helpful which is why for the ceiling in the area outside the one exactly above the table, the ceiling looks hard and reflective. This helps the cross-table conversations to reflect off of these surfaces towards the people seated away from the table and aid in speech intelligibility and allows the people to be able to listen to conversations from the table.

Reverberation time (푹푻ퟔퟎ) measurement

The reverberation time of the conference room was measured. The impulse source was a physical clap and the 30-dB decay time was first measured and multiplied by a factor of 2 to calculate the 푅푇60 reverberation time of the room. Figure 5-3 shows the sound decay measured in the conference room.

In Figure 5-3, the red line represents the 30-dB decay in sound pressure level. The 푅푇30 time can be calculated by calculating the time difference between the two points. As mentioned in the previous chapter where the reverberation time measurement of the conference room was discussed, coupling of spaces make the measurement of reverberation time difficult because it makes the slope of the decay curve change depending on the different reverberation characteristics of the coupled spaces adjacent to the room being measured. In this measurement, the excitation achieved in the sound field was about 60-dB above the noise floor. Measuring a 60- dB decay should have been possible within this dynamic range. However, the room is not perfectly isolated from the surrounding spaces and is coupled with spaces adjacent to this room.

This coupling of spaces causes the slope of the decay curve to change before the 68-dB point and after the 38-dB point. Due to this only the 푅푇30 reverberation time could be measured from the curve directly. The 푅푇30 decay time can be multiplied by a factor of 2 to get the 푅푇60 reverberation time.

Figure 5-3: Reverberation time of 0.7 seconds was measured using an impulse sound source.

푅푇30 = 1.966 − 1.61 = 0.356 sec

∴ 푅푇60 = 2 × 푅푇30 = 2 × 0.356 ≈ ퟎ. ퟕ sec

The reverberation time 푅푇60 in the conference room is around 0.7 sec. Referring back to

Figure 4-2, the volume of the conference room is around 100 cu. m. and according to the graph the reverberation time needs to be around 0.6 seconds. The calculated reverberation time of the conference room is very close to the reference.

Preliminary calculations

The preliminary calculations regarding the conference room were based on physically measured dimensions, to estimate the acoustic features of the room. The measured dimensions of the conference room were 20.3x18.8x8.5 feet or 6.1x5.77x2.72 meters. As mentioned earlier, these dimensions provide the volume estimate of an empty room which just helps us to overestimate the features and in turn facilitate better measurements by ensuring that measurements are done in the desired reverberant sound field by a safe margin.

Based on the measured dimensions The volume of the conference room, turns out to be

95.73 cu. meters.

Using equation 2.3 for critical distance,

2 × 95.73 푑푐 = 0.057 × √ 0.48

∴ 푑푐 = 1.14 meters = ퟑ. ퟕퟒ feet

According to the calculated value for critical distance, the microphones were placed at a distance more than 3.7 feet away from the sound source to ensure that their position in the reverberant field.

Also using equation 2.5 to calculate Schroeder frequency,

0.48 푓 = 2000 × √ 푠 95.73

∴ 푓푠 ≈ ퟏퟒퟐ Hz

Background noise measurement

HVAC systems were present and operating in the room. Even though the conference room seemed quiet, it was important to keep track of the background noise. Figure 5-4 shows the spectral density of the room in the absence of an excitation source. The important thing to note, regarding the background noise in the room, is the decrease in level with increasing frequency.

Above 200 Hz, the spectral density for the entire frequency range up to 2 KHz decays significantly and hence, it can be said that a good signal to noise ratio can be ensured in the frequency range of interest that is from 200 Hz to 2000 Hz.

Figure 5-4: Spectral density of the background noise in the conference room showing the frequency content without any external sound source.

38 Comparison measurement

The conference room was the second room to be measured. Figures 5-5 and 5-6 include all the spectral densities of all the recorded files plotted on a single graph, categorized depending on the recording conditions – stationary or perturbed. The bold graph in each figure represents the averaged power spectral density of the 8 responses.

Figure 5-5: Figure shows the comparison between the individual spatial points and the Averaged spectral density for the 8 spatial points measured in the stationary condition.

Figure 5-6 Figure shows the comparison between the individual spatial points and the Averaged spectral density for the 8 spatial points measured in the perturbed condition.

39 Figure 5-7 shows the two averaged spectral densities calculated in the stationary as well as perturbed conditions compared against each other on a single plot. Though the two conditional measurements do not deviate too much from each other, the graph shows slight differences between the two.

Figure 5-7: Average spectral densities of the stationary and perturbed measurements compared against each other in the frequency range from 200 Hz to 2000 Hz.

The comparison plot will be zoomed in to show a frequency range of 50 Hz. Figures 5-8 a and 5-8 b show the comparison plot zoomed in from 530 Hz to 610 Hz and 1180 Hz to 1260 Hz respectively. Looking at both the figures the stationary and the perturbed measurement are not exactly equal and there are definite differences in the two conditional measurements. In Figure 5-

8 a, from 530 Hz to around 555 Hz, the perturbed measurement shows an enhanced frequency response.

Figure 5-8: Zoomed in responses of the stationary and the perturbed conditions plotted together show the differences between the measurements made in the stationary and perturbed condition. a) from 530 to 610 Hz (left figure), b) from 1180 Hz to 1260 Hz (right figure)

However, from 555 Hz to around 570 Hz the frequency responses follow same shape but do show minor differences in amplitude. In Figure 5-8 b, from around 1200 Hz to 1210 Hz, the perturbed condition shows a reduction in the amplitude as compared to the stationary measurement but in the lower frequencies from 1180 to 1190 Hz, the perturbed measurement is seen to have a greater amplitude than the stationary measurement. Above 1230 Hz, both the responses of the stationary as well as the perturbed measurements follow a similar shape with minor changes detected around 1245 Hz.

Figure 5-9 shows a zoomed in image of the frequency responses of the stationary as well as the perturbed condition from 1860 Hz to 1940 Hz. Even in the higher frequency range, the comparison shows differences similar to the ones seen in the lower frequency ranges. From 1860

Hz to 1875 Hz, the response in the perturbed measurement seems to be slightly bigger in amplitude as compared to the stationary measurement. Above 1875 Hz, the responses of both the stationary and perturbed measurements follow each other closely with minor shifts in amplitude like around 1900 Hz, 1907 Hz and 1918 Hz. Above the frequency of 1925 Hz up to 1940 Hz, the

41 perturbed condition response shows increase in amplitude as compared to the response of the stationary condition.

Figure 5-9: Zoomed in responses of the stationary and the perturbed conditions plotted together show the differences between the measurements made in the stationary and perturbed condition from 1860 Hz to 1940 Hz.

Figures 5-9 a and 5-9 b show the standard deviation of the 8 individual measurements from the average of all the spatial points measured in the stationary and perturbed conditions, respectively. Three curves are plotted on the same graph in these figures. The black curve represents the average spectral density of the 8 spatial points. The orange curve is the result of the addition of the calculated standard deviation and the average spectral density and the pink curve is the result of subtraction of the calculated standard deviation from the average spectral density.

Figure 5-10: The standard deviation calculated in the two conditional measurements show differences across the shown frequency range but do not show much difference in amplitude. a) stationary condition (left figure), b) perturbed condition (right figure)

Figures 5-10 a and 5-10 b show the difference between the two standard deviation curves measured in the stationary and the perturbed condition respectively. To say that the perturbed condition improves the measurement by making the field more diffuse, the difference between the two standard deviation curves needed to be smaller as compared to the calculated standard deviation curves measured in the stationary condition.

Figure 5-11: The calculated difference between the two standard deviation curves. a) stationary condition (left curve), b) perturbed condition (right curve)

43 According to the theory, the standard deviation calculated in the perturbed condition should be significantly smaller than the stationary condition.

From the figures, it can be observed that in the perturbed condition the standard deviation is less than that in the stationary condition. However, the reduction in the standard deviation is small. The goal of this study was to check whether by perturbing the sound field, the standard deviation becomes closer to the average spectral density curve or not. Also, the variation across the deviation in across the frequency axis should have reduced significantly to be able to conclude whether the perturbations in the sound field made a big difference in the measurements or not. Comparing the calculated standard deviation of the stationary and perturbed measurements, it can be said that perturbing the sound field in the 2nd floor conference room in the Applied Science building did not conform to the theory which incited this research study.

Chapter 6

Room #22 (Hammond Building) – Data Analysis

General construction and features

Room #22 located in the Hammond building on the University Park Campus of the

Pennsylvania State University is a large room, mostly used for storage. Sections of this room are used by different departments for carrying out small studies or non-acoustical measurements. The volume of the room is large and the construction of the room on all sides is hard and reflecting.

The floor, walls and the ceiling have little to no absorption. This in turn increases the reverberation time of the room, referring to Sabine’s formula stated in equation 2.2.

Figures 6-1 and 6-2 show a few pictures taken in the room. The figures show the different objects present in the room. The number of objects present in the room make the measurements difficult and limits the space which can be measured. To get measurements in this room, the passageway as seen in Figure 6-2, which was about 5 to 6 feet wide was used and the spatial points chosen were spread along these passageways.

Another challenge in terms of height was the limitation in the equipment being used. The height of the room is around 25 feet while the maximum height reached by microphone stands was about 7 feet. Therefore, there was a sound space above this reachable height which could not be measured. This room was a challenge to carry out measurements in a similar manner as the ones carried out in the other rooms. However, this room was particularly chosen because the next phase of the study that Miller [1] conducted in the reverberation chamber is going to be moved to this room. Therefore, it was important to understand the sound field and to examine whether the measurements in this room could be improved than the ones done in the reverberation chamber.

Figure 6-1: Room #22 in Hammond building is cluttered with many objects.

Figure 6-2: Microphones were set up in the free spaces between the objects.

Reverberation time (푹푻ퟔퟎ) measurement

The reverberation time of the room #22 in Hammond building was measured in a similar way as the conference room. The impulse source was a physical clap and the 20-dB decay time was first measured and multiplied by a factor of 3 to calculate the 푅푇60 reverberation time of the room. Figure 6-3 shows the sound decay measured in room #22 in Hammond building.

In Figure 6-3, the red line represents the 20-dB decay in sound pressure level. The 푅푇20 time can be calculated by calculating the time difference between the two points. As mentioned in the previous chapter where the reverberation time measurement of the conference room was discussed, coupling of spaces make it difficult to measure the reverberation time because it makes the slope of the decay curve change depending on the different reverberation characteristics of the coupled spaces adjacent to the room being measured. In this measurement, the excitation achieved in the sound field was about 50-dB above the noise floor. Measuring a 30-dB decay should have been possible within this dynamic range. However, the room is not perfectly isolated from the surrounding spaces but is coupled with spaces adjacent to this room. This coupling of spaces causes the slope of the decay curve to change before the 67-dB point and also after the 47- dB point. Due to this only the 푅푇20 reverberation time could be measured from the curve directly.

The 푅푇20 decay time can be multiplied by a factor of 3 to give the 푅푇60 reverberation time.

Figure 6-3: A reverberation time of 1.3 seconds was measured in the room #22.

푅푇20 = 3.683 − 3.228 = 0.455 푠푒푐

∴ 푅푇60 = 3 × 푅푇20 = 3 × 0.455 ≈ ퟏ. ퟑퟕ 푠푒푐

The reverberation time 푅푇60 in room #22 was found to be around 1.37 sec. The reverberation time for room #22 was longer than the conference room because of the volume of the room and low absorption in the room as mentioned earlier.

Preliminary calculations

As compared to the conference room, room #22 in Hammond building is considerably large. Therefore, unlike the conference room it was not possible to measure the volume of this room physically and the dimensions of the room were taken from the data that is on file with the person in charge of the facility. The dimensions of the room in the database are 42x26x25 feet.

Using these dimensions, the volume of the room #22, when empty, amounts to 773.05 cu. m.

Figures 6-1 and 6-2 show that the room is populated with a lot of objects which reduces the volume of the room. This volume estimate results in the over-estimation of the critical distance and hence allowing the microphones to be placed further into the reverberant field as discussed in chapter 3.

Using equation 2.3 to calculate critical distance,

2 × 773.05 푑푐 = 0.057 × √ 1.37

∴ 푑푐 = 1.92 meters = ퟔ. ퟑ feet

According to the calculated critical distance, the microphones were placed more than 6.3 feet away from the sound source to ensure that they were placed in the reverberant field. Room

#22 is large and hence it was possible to have the distance between the source and the microphones be more than 6.3 feet.

48 Also using the equation 2.5 to calculate Schroeder frequency,

1.37 푓 = 2000 × √ 푠 773.05

∴ 푓푠 ≈ ퟖퟒ Hz

Background noise measurement

Room #22 is not designated for any special purpose, other than being a large room available to people at different times, whose work is not affected much by the sound field in the room. It can be considered as a laboratory space for several teams from different departments.

Hence, little attention is given to taking care of the sound field in the room. All the walls and the ceiling are made up of hard surfaces and there is not much isolation to external noise. In such conditions, it was essential to keep a track of the background noise signals in the room.

Figure 6-4 shows the background noise spectrum measured for room #22. Figure 6-5 shows the zoomed in background noise spectrum focused on the low frequency range. Looking at the background noise spectral density up to 2000 Hz, the background noise decreases as the frequency increases. It was necessary to get this information to ensure good signal to noise ratio is achieved in the frequency range of interest.

Figure 6-5 shows the zoomed in spectral density up to 400 Hz. The background noise has a high amplitude as can be observed in Figure 6-4 but the zoomed in image in Figure 6-5 shows some sharp peaks found at some frequencies especially at 40 Hz, 120 Hz, 200 Hz and 240 Hz.

Due to the presence of sharp peaks in the background noise of room #22 the frequency range of interest for the measurements conducted in this room was slightly modified to be 300 Hz to 2000

Hz.

Figure 6-4: Spectral density of the background noise in room #22 showing the frequency content without any external sound source.

Figure 6-5: Spectral density zoomed in up to a 400 Hz to analyze the low frequency content.

50 Comparison measurement

Since, the volume of the room was large, the space available for measurements was also big even with the presence of many objects. Figures 6-6 and 6-7 show the spectral averages of the spatial points (black curve) plotted along with the spectral densities of the individual spatial points (grey curves) measured under stationary and perturbed conditions, respectively.

Figure 6-6: Average spectral density versus individual spectral densities measured in the stationary condition.

Figure 6-7: Average spectral density versus individual spectral densities measured in the perturbed condition.

51 Figure 6-8 shows the two averaged spectral densities calculated in the stationary as well as perturbed conditions compared against each other on a single plot. Though the two conditional measurements do not deviate too much from each other, the graph shows slight difference between the two.

Figure 6-8: Average spectral densities compared against each other in the frequency range from

300 Hz to 2000 Hz.

To be able to look at the difference in more detail, the comparison plot will be zoomed in to show a frequency range of 50 Hz to be able to look at the differences more closely. Figures 6-9 a and 6-9 b show the comparison plot zoomed in from 350 Hz to 380Hz and 730 Hz to 760 Hz respectively. Looking at both the figures the stationary and the perturbed measurement are not exactly equal and there are definite differences in the two conditional measurements.

Figure 6-9: Zoomed in response of the stationary and the perturbed conditions plotted together. a) from 350 to 380 Hz (left figure), b) from 730 Hz to 760 Hz (right figure)

In Figure 6-9 a, from 340 Hz to 365 Hz, both the responses for the stationary as well as the perturbed measurements follow a similar pattern. However, the response measured in the perturbed measurement shows a slightly smaller amplitude as compared to the stationary measurement. Especially at around 365 Hz, both the response come very close and there is little difference in amplitude between the stationary and the perturbed measurement. Above 365 Hz up to 380 Hz, the responses show a good amount of deviation from each other. Particularly the perturbed measurement drops considerably in amplitude as compared to the stationary measurement.

Figure 6-9 b shows the zoomed in image of the compared responses of the stationary and the perturbed measurements from 730 Hz to 760 Hz. The feature seen throughout this frequency range of 50 Hz is very evident. The perturbed response follows the stationary response very closely in this portion of the comparison figure. Apart from minor differences in amplitude, the overall appearance for the responses for both the stationary and perturbed measurements are very similar to each other.

53 Figure 6-10 shows the responses of the stationary and the perturbed measurement in the higher frequency range of interest. The figure shows the zoomed in portion of the responses from

1975 Hz to 2010 Hz. At around 1975 Hz, both the responses come very close to each other with a minor difference in amplitude. Above 1975 Hz, the perturbed response exceeds the stationary response by a small amplitude up to a frequency of 2000 Hz. Above 2000 Hz, as seen in the figure especially from 2002 Hz to 2010 Hz, some response shape changes are seen when the perturbed measured response is compared to the stationary measured response.

Figure 6-10: Zoomed in frequency response of the stationary and perturbed measurements from

1860 Hz to 1940 Hz.

Figure 6-11 a and 6-11 b show the standard deviation of the 20 individual measurements from the average of all the spatial points measured in the stationary and perturbed conditions, respectively. Three curves are plotted on the same graph in these figures. The black curve represents the average spectral density of the 8 spatial points. The orange curve is the result of the addition of the calculated standard deviation and the average spectral density and the pink curve is the result of subtraction of the calculated standard deviation from the average spectral density.

Figure 6-11: Calculated standard deviation plotted along with the average spectral density. a) stationary condition (left figure), b) perturbed condition (right figure)

Figure 6-12 a and 6-12 b show the difference between the two standard deviation curves measured in the stationary and the perturbed condition respectively. To say that the perturbed condition improves the measurement by making the field more diffuse, the difference between the two standard deviation curves needed to be smaller as compared to the calculated standard deviation curves measured in the stationary condition. From the figures, it can be observed that in the perturbed condition the standard deviation is less than that in the stationary condition.

However, the reduction in the standard deviation is small.

Figure 6-12: The calculated difference between the two standard deviation curves. a) stationary condition (left curve), b) perturbed condition (right curve)

55 The goal of this study was to check whether by perturbing the sound field, the standard deviation becomes closer to the average spectral density curve or not. Also, the variation across the deviation in across the frequency axis should have reduced significantly to be able to conclude whether the perturbations in the sound field made a big difference in the measurements.

Comparing the calculated standard deviation of the stationary and perturbed measurements, it can be said that perturbing the sound field in the room #22 in Hammond building did not conform to the theory which incited this research study.

Chapter 7

Reverberation chamber – Data analysis

General construction and features

The reverberation chamber was the first room that was measured among the 4 rooms that were selected. The measurements kicked off with the reverberation chamber because Miller [1] had difficulties while conducting his measurements in the reverberation chamber. Figure 7-1 shows the reverberation chamber located adjacent to the anechoic chamber on the University park campus of the Pennsylvania State University. The reverberation chamber is not used as much as the anechoic chamber because of challenges that it brings along with it.

Figure 7-1: General construction and characteristics of the Reverberation chamber.

Figure 7-1 shows the general structural characteristics of the room. The room is perfectly rectangular and the walls, ceiling and the floor are made up of hard reflecting surfaces. Therefore, the reverberation time is big even if the volume of the room is small compared to room #22 referring back to Sabine’s formula mentioned in equation 2.2.

Reverberation time (푹푻ퟔퟎ) measurement

The impulse source was a physical clap and the 30-dB decay time was first measured and multiplied by a factor of 2 to calculate the 푅푇60 reverberation time of the room. Figure 7-2 shows the sound decay measured in the reverberation chamber. In Figure 7-2, the red line represents the

30-dB decay in sound pressure level. The 푅푇30 decay time can be calculated by calculating the time difference between the two points.

As mentioned in the previous chapter where the reverberation time measurement of the conference room was discussed, coupled spaces make it difficult to measure the reverberation time because it results in the slope of the decay curve to change depending on the different reverberation characteristics of the coupled spaces adjacent to the room being measured. In this measurement, the excitation achieved in the sound field was about 55-dB above the noise floor.

The room is not perfectly isolated from the surrounding spaces but is couple with spaces adjacent to the room. This coupling of spaces causes the slope of the decay curve to change before the 75- dB point and also after the 45-dB point. Due to this only the 푅푇30 reverberation time could be measured from the curve directly. The 푅푇30 decay time can be multiplied by a factor of 2 to give the 푅푇60 reverberation time.

푅푇30 = 11.66 − 9.628 = 2.032 sec

∴ 푅푇60 = 2 × 푅푇30 = 2 × 2.032 ≈ ퟒ. ퟎퟔ sec

The 푅푇60 reverberation time in the reverberation chamber is around 4 seconds, which is bigger as compared to any room of this size. Therefore, sound energy that enters the reverberation chamber takes a long time to decay.

Figure 7-2: A reverberation time of 4 seconds was measured in the reverberation chamber.

Preliminary calculations

The reverberation chamber has a large reverberation time but is actually a small room in size but bigger than the conference room studied in chapter 5. It was possible to physically measure the length and the width of the chamber. The dimensions of the chamber were

22.08x18.75x10 feet or 6.731x5.715x3.048 meters. Using these dimensions, the volume can be calculated which is about 117.25 cu. m. This value was used to calculate the critical distance and

Schroeder frequency.

Using equation 2.3 for the formula for critical distance,

2 × 117.25 푑푐 = 0.057 × √ 4.06

∴ 푑푐 = 0.43 meters = ퟏ. ퟒퟏ feet

59 Also using the equation 2.5 to calculate Schroeder frequency,

4.06 푓 = 2000 × √ 푠 117.25

∴ 푓푠 ≈ ퟑퟕퟐ Hz

In the conference room and room #22 in Hammond building, the critical distance was over-estimated because of the calculated volume being slightly bigger than the actual volume.

However, in this case, the calculated volume is very close to the actual volume and hence to ensure the placement of microphones in the reverberant field, the distance between the sound source and microphones was bigger than the calculated critical distance that is 1.41 feet.

Background noise measurement

The reverberation chamber is one of the two unique enclosures that can be used to simulate enclosures with properties that are not possible in the real world. In addition to that, the reverberation chamber on the University Park campus is located right next to the anechoic chamber and the door of the reverberation chamber opens into the anechoic chamber. Since the anechoic chamber is heavily used, the door separating the two chambers is heavy as well as has a tight seal to avoid sound transmission between the two rooms.

However, the long reverberation time makes a big difference between the two chambers when it comes to noise. In the anechoic chamber, since the reverberation time is very small, the noise entering the chamber does not stay inside for long but decays very quickly. However, in the reverberation chamber due to the large reverberation time, any noise entering the room stays in the chamber for a long time.

60 Figure 7-3 shows the background noise spectrum measured in the reverberation chamber up to a frequency of 2000 Hz. Some high amplitude peaks can be seen in the low frequency range around 50 Hz and 100 Hz. The low frequency noise may be due to the HVAC systems operating around the room, entering through a duct that penetrates the reverberation chamber from outside the anechoic chamber. Also, the space adjacent to the anechoic chamber is the ‘Jet Noise

Laboratory’ which conducts tests occasionally and have their own apparatus and systems used for different studies. There is a direct path from this test facility to the penetrating duct, which introduces external noise sources into the reverberation chamber whenever the ‘Jet noise lab’ is conducting tests. As seen in the Figure 7-3, above 200 Hz, the background decreases significantly in amplitude and a good signal to noise ratio can be ensured in the frequency range of interest from 200 Hz to 2000 Hz.

Figure 7-3: Spectral density of the background noise in reverberation chamber showing the frequency content without any external sound source.

Figure 7-4: Zoomed in background noise spectral density of the reverberation chamber.

Comparison measurement

The volume of the reverberation chamber is smaller than room #22 but the room is nearly empty. Also, the calculated critical distance is 1.41 ft. due to which a lot of spatial points could have been chosen for measurements. As mentioned earlier, the reverberation chamber was the first room to be measured and studied among the 4 rooms. At this early phase, the study and the process of measurement were still being set up and finalized. Therefore, only 4 spatial points were measured in the reverberation chamber. As the study progressed further, the number of spatial points measured increased depending on the volume and space available for measurements in the rooms.

62 Figures 7-5 and 7-6 show the spectral averages of the spatial points (black curve) plotted along with the spectral densities of the individual spatial points (grey curves) measured under stationary and perturbed conditions, respectively.

Figure 7-5: Average spectral density (bold black curve) versus individual spectral densities (gray curves) measured in the stationary condition.

Figure 7-6: Average spectral density (bold black curve) versus individual spectral densities (gray curves) measured in the perturbed condition.

63 Figure 7-7 shows the two averaged spectral densities calculated in the stationary as well as perturbed conditions compared against each other on a single plot. Though the two conditional measurements do not deviate too much from each other, the graph shows slight difference among the two.

Figure 7-7: Average spectral densities compared against each other in the frequency range from

200 Hz to 2000 Hz.

To be able to look at the difference in more detail, the comparison plot will be zoomed in to show a frequency range of 50 Hz to be able to look at the differences more closely. Figures 7-8 a and 7-8 b show the comparison plot zoomed in from 250 Hz to 300 Hz and 1070 Hz to 1100 Hz respectively. Looking at both the figures, the stationary and the perturbed measurement are not exactly equal and there are differences in the two conditional measurements.

Figure 7-8: Zoomed in response of the stationary and the perturbed conditions plotted together. a) from 250 to 290 Hz (left figure), b) from 1070 Hz to 1100 Hz (right figure)

In Figure 7-8 a, from 250 Hz to about 262 Hz, the perturbed measurement seems to be lowered in amplitude as compared to the stationary condition. At about 263 Hz, there is a sharp spike where the amplitude of the perturbed conditional measurement is seen to have increased above the stationary measurement. The amplitude of the response measured from 270 Hz to 277

Hz shows that the perturbed condition has a higher amplitude as compared to the stationary condition. Following this, the amplitude of the response for the perturbed measurement drops below the stationary measurement after which above 282 Hz up to 286 Hz the perturbed measurement is seen to be bigger in amplitude than the stationary measurement, also seen above

290 Hz.

In Figure 7-8 b, the amplitude of the measured response in the perturbed condition is seen to be greater than the stationary measurement up to a frequency of 1075 Hz. Above this frequency the perturbed conditional response drops below the stationary condition. Apart from the major part of this figure where the amplitude of the response measured in the perturbed condition is seen to be lower than the stationary measurement, at some individual frequencies like

1082 Hz, 1087 Hz, 1092 Hz, 1094 Hz and 1099 Hz, the measured response of the perturbed measurement is seen to be greater than the amplitude of the response measured in the stationary

65 condition. At 1096 Hz, the responses measured in the stationary as well the perturbed condition is seen to be very close in value even if the shape of the responses differ from each other.

Figure 7-9 shows the responses of the stationary and the perturbed measurement in the higher frequency range of interest. The figure shows the zoomed in portion of the responses from

1945 Hz to 1993 Hz. In the frequency ranges of 1952 Hz to 1957 Hz, 1961 Hz to 1967 Hz, 1970

Hz to 1976 Hz, 1982 Hz to 1985 Hz and also at individual frequencies 1978 Hz and 1987 Hz, the response measured in the perturbed condition is seen to be higher than the stationary conditional measurement. On the contrary in the frequency ranges of 1967 Hz to 1970 Hz, 1989 Hz to 1992

Hz and also at individual frequencies 1982 Hz and 1986 Hz the response measured in the perturbed condition is seen to be lower than the response measured in the stationary condition.

Figure 7-9: Zoomed in frequency response of the stationary and perturbed measurements from

1945 Hz to 1993 Hz.

Figure 7-10 a and 7-10 b show the standard deviation of the 4 individual measurements from the average of all the spatial points measured in the stationary and perturbed conditions, respectively. Three curves are plotted on the same graph in these figures. The black curve represents the average spectral density of the 8 spatial points. The orange curve is the result of the addition of the calculated standard deviation and the average spectral density and the pink curve is the result of subtraction of the calculated standard deviation from the average spectral density.

Figure 7-10: Calculated standard deviation plotted along with the average spectral density. a) stationary condition (left figure) b) perturbed condition (right figure)

Figure 7-11 a and 7-11 b show the difference between the two standard deviation curves measured in the stationary and the perturbed condition respectively. To say that the perturbed condition improves the measurement by making the field more diffuse, the difference between the two standard deviation curves needed to be smaller as compared to the calculated standard deviation curves measured in the stationary condition.

Figure 7-11: The calculated difference between the two standard deviation curves. a) stationary condition (left curve), b) perturbed condition (right curve)

From the figures, it can be observed that in the perturbed condition the standard deviation is less than that in the stationary condition. However, the reduction in the standard deviation is

67 small. The goal of this study was to check whether by perturbing the sound field, the standard deviation becomes closer to the average spectral density curve or not. Also, the variation across the deviation in across the frequency axis should have reduced significantly to be able to conclude whether the perturbations in the sound field made a big difference in the measurements or not. Comparing the calculated standard deviation of the stationary and perturbed measurements, it can be said that perturbing the sound field in the reverberation chamber did not conform to the theory which incited this research study.

Chapter 8

Ensemble A 132 (Music Building - II) – Data analysis

General construction and features

The music buildings I and II on the University Park campus are facilities used by the music department of the University. Majority of the rooms present in these buildings are constructed for musical use. Some are used for rehearsals while some are used for performances.

The difference between these two kinds of rooms is the presence or absence of an audience.

When the performance hall is filled with an audience, the absorption characteristics of the room changes as compared to the room when empty.

Figure 8-1 shows the room A 132 and its physical characteristics. The room has hard floor, ceiling and walls and has very little furniture or objects. Such a large room with these characteristics is bound to have a large reverberation time referring back to Sabine’s formula mentioned in equation 2.2, which is unfavorable for music rehearsals.

Figure 8-1: Acoustic treatments on the ceiling and walls of Ensemble 132 (Music – Building II).

69 Referring to Figure 4-2 where Long [4] graphically represented the reverberation times for rooms constructed for various purposes depending upon their volume, the reverberation time for a room emphasizing concert hall music needs to be between 1.4 and 1.6. Long [4] in his book also mentioned how in the modern day, because of sound reinforcement systems and their ability to add the reverberation effects electronically, the reverberation times for spaces has gone down as compared to what he has suggested in his book.

To have an appropriate reverberation time in the room ensemble A 132, the room has been acoustically treated. As seen in the figures, all four walls are covered with acoustic panels in a checkered pattern. Acoustic clouds are installed underneath the ceiling which absorb sound and hence reduce reflections from the ceiling. The walls have curtains that are thick and heavy to move. These curtains can be moved to cover the walls and further increase absorption and decrease the reverberation time.

During the measurements, the position of the curtains was just as seen in the figures. The objects present in the room consisted of stacked chairs and music stands next to the walls, a piano and a harp stored in a box. Since the room was large and objects were placed far enough along the perimeter to leave enough space in the center of the room, there were enough spatial points that could be measured in this room without getting close to the objects. The number of spatial points measured in this room was 30. Each spatial point was more than 6 feet away from the next.

Reverberation time (푹푻ퟔퟎ) measurement

The impulse source was a physical clap and the 30-dB decay time was first measured and multiplied by a factor of 2 to calculate the 푅푇60 reverberation time of the room. Figure 8-2 shows the sound decay measured in the reverberation chamber. In figure 8-2, the red line represents the

30-dB decay in sound pressure level. The 푅푇30 decay time can be calculated by calculating the time difference between the two points.

Figure 8-2: A reverberation time of 1.6 seconds was measured in the room Ensemble A 132.

푅푇30 = 1.922 − 1.082 = 0.84 sec

∴ 푅푇60 = 2 × 푅푇30 = 2 × 0.84 = ퟏ. ퟔퟖ sec

The reverberation time 푅푇60 in the room ensemble A 138 is 1.68 sec. which is small as compared to other rooms with similar dimensions and properties. Long [4] shows that the reverberation time for a space utilized for classical music or concert halls, having volume greater than a 1000 cu. m. should be between 1.4 and 1.6 seconds with having a 5 to 10 percent variation from the ideal values to be a common trend.

71 Preliminary calculations

The room is a large enclosure which makes it difficult to measure the dimensions physically. Therefore, the dimensions of the room were taken from the records on file of the person in charge of the facility. Unlike the room #22 in Hammond building which was densely populated with objects, Ensemble A #132 is scarcely populated with objects. The calculated volume based on the dimensions is very close to the actual volume with the objects in the room.

Hence, the estimated critical distance won’t be an over-estimation unlike some of the rooms measured before. Therefore, the distance maintained between the sound source and the microphones was a little over the calculated critical distance, to ensure that the microphones are always placed in the reverberant field of the room.

Referring to the floor plan made available by the music department, the geometry of the room is not perfectly rectangular. The approximate dimensions of the room are

41x40x24.83 feet and the calculated volume of the room turns out to be around 1126.03 cu. m.

This calculated volume was used to calculate the critical distance and the Schroeder frequency.

Using equation 2.3 to calculate critical distance

2 × 1126.03 푑푐 = 0.057 × √ 1.68

∴ 푑푐 = 2.09 meters = ퟔ. ퟖퟕ feet

Also using equation 2.5 to calculate Schroeder frequency,

1.68 푓 = 2000 × √ 푠 1126.03

∴ 푓푠 ≈ ퟕퟕ. ퟐퟓ Hz

72 Background noise measurement

The room ensemble A 132 located inside Music building – II is connected to other rehearsal rooms by a corridor. The door at the entrance of the room is able to provide some isolation from the noise entering the room from outside but some noise sources with high sound pressure level are still heard inside the room even with the door closed. For example, during the experimental set up, before taking the measurements, a musician was rehearsing on a piano in the room across the room A 132. Though not as loud, the sound was clearly heard inside the room.

Figure 8-3 shows the measured spectral density of the background noise of the room in the absence of an external sound source. The major portion of the background noise lies in the lower frequency range. The background noise in the frequency range of interest from 200 Hz to

2000 Hz is seen to decay significantly as the frequency increases and hence a good signal to noise ratio can be ensured in this frequency range of interest.

Figure 8-3: Spectral density of the background noise in the room Ensemble A 132 showing the frequency content without any external sound source.

73 Also Figure 8-4 shows the zoomed in spectral density of the background noise in the higher frequency range. Though the amplitude at these higher frequencies is lower than the ones observed at the lower frequencies, the sharp peaks seen in this higher frequency range from 10

KHz to 22 KHz were peculiar in this room. Referring to the figure, sharp peaks were seen above

14 KHz. The highest amplitude among this set of peaks was seen around 15.3 KHz. Also, some sharp peaks were seen in the higher frequency range above 21.3 KHz. Though the source of these frequencies cannot identified, they maybe related to fire alarm systems present in the room.

Figure 8-4: Zoomed in Background noise spectral density above 10 KHz of room ensemble A

132.

Comparison measurement

Figures 8-5 and 8-6 are the spectral averages of the 30 spatial points (black curve) plotted along with the spectral densities of the individual spatial points (gray curves) measured under stationary and perturbed conditions, respectively.

Figure 8-5: Average spectral density (bold black curve) versus individual spectral densities (gray curves) measured in the stationary condition.

Figure 8-6: Average spectral density (bold black curve) versus individual spectral densities (gray curves) measured in the stationary condition.

75 Figure 8-7 shows the two averaged spectral densities calculated in the stationary as well as perturbed conditions compared against each other on a single plot.

Figure 8-7: Average spectral densities compared against each other in the frequency range from

200 Hz to 2000 Hz.

To be able to look at the difference in more detail, the comparison plot will be zoomed in to be able to look at the differences more closely. Figures 8-8 a and 8-8 b show the comparison plot zoomed in from 440 Hz to 480 Hz and 990 Hz to 1040 Hz respectively.

Figure 8-8: Zoomed in response of the stationary and the perturbed conditions plotted together. a) from 250 to 290 Hz (left figure), b) from 1070 Hz to 1100 Hz.

In Figure 8-8 a, both the responses measured in the stationary and perturbed conditions follow each other very closely. There is very little difference in the amplitude between the two responses. The overall shape also nearly is the same between the two conditional measurements, throughout the frequency range from 440 Hz to 480 Hz. In Figure 8-8 b, similar to Figure 8-8 a, both the responses measured in the stationary and the perturbed condition follow a similar shape.

There is very little difference in terms of the overall shape of the responses. At frequencies, 1001

Hz, 1005 Hz and in the frequency range of 1025 to 1030, the amplitude of the measured responses in the stationary and the perturbed condition are nearly the same. On the other hand, elsewhere in the frequency range from 980 Hz to 1030 Hz, the amplitude of the response measured in the perturbed condition is slightly greater than the amplitude of the response measured in the stationary condition.

Figure 8-9 shows the responses of the stationary and the perturbed measurement in the higher frequency range of interest. The figure shows the zoomed in portion of the responses from

1810 Hz to 1860 Hz. Similar to the trend observed in Figure 8-8, the overall shape is nearly the same for the responses measured in the stationary as well as the perturbed condition. At frequencies 1827 Hz, 1854 Hz, 1855 Hz and 1856 Hz, the amplitude for both the responses of the

77 stationary as well as perturbed conditional measurements is equal. On the other hand, elsewhere in the frequency range from 1810 Hz to 1860 Hz, the amplitude of the response measured in the perturbed condition is slightly greater than the amplitude of the response measured in the stationary condition.

Figure 8-9: Zoomed in frequency response of the stationary and perturbed measurements from

1810 Hz to 1860 Hz.

Figure 8-10 a and 8-10 b show the standard deviation of the 30 individual measurements from the average of all the spatial points measured in the stationary and perturbed conditions, respectively. Three curves are plotted on the same graph in these figures. The black curve represents the average spectral density of the 8 spatial points. The orange curve is the result of the addition of the calculated standard deviation and the average spectral density and the pink curve is the result of subtraction of the calculated standard deviation from the average spectral density.

Figure 8-10: Calculated standard deviation plotted along with the average spectral density. a) stationary condition (left figure), b) perturbed condition (right figure)

Figure 8-11 a and 8-11 b show the difference between the two standard deviation curves measured in the stationary and the perturbed condition respectively. To say that the perturbed condition improves the measurement by making the field more diffuse, the difference between the two standard deviation curves needed to be smaller as compared to the calculated standard deviation curves measured in the stationary condition.

Figure 8-11: The calculated difference between the two standard deviation curves. a) stationary condition (left curve), b) perturbed condition (right curve)

From the figures, it can be observed that in the perturbed condition the standard deviation is less than that in the stationary condition. However, the reduction in the standard deviation is

79 small. The goal of this study was to check whether by perturbing the sound field, the standard deviation becomes closer to the average spectral density curve or not. Also, the variation across the deviation in across the frequency axis should have reduced significantly to be able to conclude whether the perturbations in the sound field made a big difference in the measurements or not. Comparing the calculated standard deviation of the stationary and perturbed measurements, it can be said that perturbing the sound field in the room ensemble A 132 in music building-II did not conform to the theory which incited this research study.

Chapter 9

Conclusion

This research study was motivated by the private conversation that Arthur H. Benade had with Dr. Stephen Thompson. Benade’s theory suggested that if the sound field is perturbed while taking a measurement, the time-averaged analysis of that measurement will improve the measurements by making the sound field diffuse. If this theory holds true, in the perturbed conditional measurements, the standard deviation curves measured from the averaged spectral densities should become less than the deviations measured in the stationary condition and should come very close to the curve of the average of the spectral densities of all the spatial points measured. On the other hand, a null result can be expected in spaces that were diffuse to begin with, that is perturbing the sound field in these spaces would result in no change. The rooms measured in this research study showed notable spatial and spectral features which indicates that they were not perfectly diffuse.

In this study, 4 rooms located on the University Park campus of the Pennsylvania State

University were measured. All the 4 rooms differed from each other in terms of constructional and acoustical characteristics as seen in Table 1-1 in chapter 1. Several spatial points were measured in all the 4 rooms and the calculated spectral densities of the stationary and the perturbed measurements were compared against each other.

Referring to the comparison between the spectral densities of the 4 rooms in chapters

5,6,7 and 8, the Conference room, room #22 in Hammond building and the Reverberation

Chamber show both similarities and differences. There were frequencies where in both the stationary and perturbed conditions, the averaged spectral density curves follow a similar shape

81 and at some frequencies, the amplitude for both the measurements are same as well. Also, there were frequencies, where the spectral density measured in the perturbed condition seemed to deviate from the spectral density measured in the stationary condition. The differences seen were in terms of amplitude when the two average spectral densities were compared on a single graph.

In room Ensemble A 132 – music building - II, over most of the frequency range, the calculated spectral densities for both the stationary as well as the perturbed conditions followed each other closely and the amplitude difference was small.

The difference between the first 3 rooms measured and the room ensemble A 132 was the space available for perturbations. The conference room and the reverberation room had a small volume and hence the perturbations in these rooms made a difference when the average spectral densities were compared. Also, in room #22 in Hammond building, even if the volume of the room is large, the space available for perturbing the room was only available between the objects stacked on either side of the passageways as mentioned in chapter 5. However, the room ensemble A132 had a large volume and was mostly empty. The space available for perturbations in this room was large and hence, perturbing in the room in one small section did not seem to affect the sound field in other parts of the room. The difference between the two conditions may increase if the amount of perturbation is increased in the room.

In addition to the comparison between the average spectral density, 2 standard deviation curves were plotted for each room for both the stationary and the perturbed conditional measurements. Also, the difference between these two standard deviation curves for each condition was plotted separately to observe the differences. The side by side comparison between the standard deviation difference curves for both the stationary and perturbed condition showed that in the perturbed conditional measurement, the deviation was smaller as compared to the stationary conditional measurement. However, the difference observed was small in amplitude.

82 In the laboratory measurements that Benade carried out, a person moving around the room was the source of perturbations which was kept unchanged in this research study as well.

Even after perturbing the room and comparing the results with the room measured in the stationary condition, the differences observed were small. Also, the standard deviation calculated for the perturbed conditional measurement was seen to be only reduced by a couple of deciBels at the most.

Considering the observations made regarding the comparison measurements conducted in the 4 rooms where the stationary conditional measurements were compared with the perturbed conditional measurements, it can be concluded that the theory put forth by Arthur H. Benade does not hold true for rooms being perturbed by a single person walking in a room. The 4 rooms measured did not conform to Benade’s predictions and it can be said that measurements done in rooms by perturbing the sound field by a single person walking in the room, will turn out to be more or less similar to the measurements conducted in the room when it is completely stationary.

Appendix

Schroeder frequency

The concept of Schroeder frequency was briefly discussed in chapter 2 where it was defined as the frequency that separates the entire frequency range of a room into two regions.

Firstly, a region where the room modes can be identified and detected experimentally and secondly a region in which the number of modes excited due to a driving frequency is so large that individual modes excited cannot be identified or experimentally detected.

Figure A-1: Frequency response of a rectangular room of volume 180 meters cubed showing modal density in the frequency range of 20 Hz to 315 Hz. (from [9] Figure 6.2)

Figure A-1 shows the frequency response of a rectangular room. The volume of the room measured was 180 meters cubed. The figure represents the modal density of the room in the frequency range of 20 Hz to 315 Hz. The Schroeder frequency of this particular enclosure was 80

Hz.

The characteristics of the room can be observed from the figure. In the frequency range of the room from 20 Hz to 80 Hz, the individual modes can be individually detected and identified. Above 80 Hz, the individual modes start getting closer to each other as the frequency increases. At a single frequency, multiple modes are excited and hence make the identification of individual modes and frequencies difficult.

84 For any enclosure, below the Schroeder frequency, the modal response of the room dominates, whereas above the Schroeder frequency, the statistical response (reverberant) of the room dominates its frequency response. In general, the Schroeder frequency is concerned with the modal density of the frequency response of an enclosure but does not give much of an idea about the diffuseness of the sound field.

In the data analysis in the previous chapters, the graphs and figures were being observed in the frequency range above the Schroeder frequency of each individual room because of the noise sources present in the room and the possibilities of this noise impacting the frequency response of the room. In figures where, the average spectral density was compared against the individual spectral densities, it can be observed that in different spatial points, the frequency spectrum varies from one point to another. Even farther beyond the Schroeder frequency, the individual spectra look very different from one another. Therefore, it is difficult to infer that beyond the Schroeder frequency, the field can be considered to be diffuse or in other words the sound energy density is same in an enclosure regardless of the spatial position.

85 Bibliography

[1] An analysis of beam forming with sparse transducer arrays for active control, Lane Miller,

2018

[2] Fundamentals of Musical Acoustics, Arthur H. Benade, 1976 Oxford University Press, section

11.5, p.183

[3] Room Acoustics, Sixth Edition, Heinrich Kuttruff 2016

[4] Architectural Acoustics, Marshall Long 2005

[5] Recording Studio Design, 3d ed., Philip Newell, Focal Press 2013

[6] Audio Engineering Handbook, A Benson, K.B. 188 McGraw-Hill, ch. 13, eq. 13.6

[7] F. Alton Everest and Ken C. Pohlmann, Master Handbook of Acoustics, 5th Ed., (McGraw-

Hill, 2009) p. 229 — Figure 13.5

[8] ACS 597: Signal Analysis, Lecture Notes, Thomas Gabrielson Fall 2017

[9] Engineering Noise Control: Theory and Practice, David A. Bies and Colin H. Hansen, 4th Ed.,

(E&FN Spon, 2009), p.292

[10] Handbook of noise and vibration control, Malcolm J. Crocker, Wiley 2007

[11] Acoustics and Vibration of Mechanical Structures—A Herisanu, N.A Marinca, V. 2017

Springer International Publishing, p.118

[12] Sound Systems: Design and Optimization: Modern Techniques and Tools for Sound System

Design and Alignment, A McCarthy, B.2012 Taylor & Francis, ch. 3, section 3.2.3