RECENT ADVANCES in ACOUSTICS & MUSIC

Measurement of the sound-absorption coefficient on using the Tone Burst Method

QUINTERO RINCON ANTONIO Departamento de Ingeniería Electrónica Instituto Tecnológico de Buenos Aires Av. Eduardo Madero 399 ARGENTINA [email protected]

Abstract: A low-cost solution for noise level reduction in an enclosed space, such as a room, is the installation of egg materials or fruits materials (for example apple, pear or peach tree). The Tone Burst method may be used to measure the sound absorption coefficient of a material at any desired angle of incidence. The goal for this is to demonstrate that egg cartons are a myth when they are used to reduce sound level in an enclosed space.

Key-words: Tone Burst – Absorption Materials – Reflection Factor - Egg Cartons – NRC - Sound Power Level.

1. Introduction incident waves. On the contrary, if a material absorbs all incident sound, its The basic parameters of acoustic materials absorption coefficient is 1. An opposite are impedance and surface shape. Other coefficient τ, denotes reflection of sound information such as angle-dependent waves on a surface. If the reflection impedance, porosity, and tortuosity are coefficient is near zero, then the transmitted required. Material data include all energy is minor. Therefore, both necessary information essential to calculate coefficients range between 0 and 1. See reflected and transmitted field. In many figure 1. sound prediction cases, however, the Er: Reflected Energy absorbed or transmitted energy is a Er Ea sufficient quantity [1]. Ei: Incident Energy The law of the conservation of energy states Et Et: Transmitted Energy that energy can neither be created nor destroyed, but it can be changed from one Ea: Absorbed Energy Ea form to another. Absorption converts sound Ei energy into heat energy. It is useful when reducing sound levels within rooms but not Absorption coefficient range 0 ≤ α ≤ 1 Æ α = Ea / Ei

between rooms. Each material interacting Reflection coefficient range 0 ≤ τ ≤ 1 Æ τ = Et / Ei with a sound wave absorbs some sound. The most common measure is the absorption coefficient, typically denoted by Fig. 1. Sound Absorption and Sound the greek letter α. The absorption Reflection coefficient is a ratio of absorbed (Ea) to In practice, all materials absorb some incident sound energy (Ei). The reflect sound, so this is a theoretical limit [2]. coefficient is a ratio of reflect (Er) to Sound absorptive materials are widely used incident sound energy (Ei). A material with for the control of noise in a variety of an absorption coefficient of 0 reflects all different situations. Sound-absorptive

ISSN: 1790-5095 24 ISBN: 978-960-474-192-2 RECENT ADVANCES in ACOUSTICS & MUSIC

materials exist in many different forms: -fiber materials, open-cell acoustical foams, fiber board, hanging baffles, felt Fig 2. Egg Carton materials, curtains and drapes, thin porous Similarly, acoustic foam tiles help in sound sheets, head liners, carpets and hollow absortion and the limitation of acoustic concrete blocks with a small opening to the resonance have a similar characteristic to outside – to create a Helmholtz resonator. egg . For that reason, egg One characteristic common to nearly all mattresses are occasionally used as an sound-absorptive materials is that they are inexpensive substitute [4]. porous. That is, there is air flow through the material as a result of a pressure difference Sound absorption coefficients are between the two sides of the material. frequently measured in octave bands, and Porous materials are frequently fragile, and, the noise reduction coefficient (NRC) is the as a result, it is necessary to protect the average absorption in the 250 Hz, 500 Hz, exposed surface of the material. Typical 1000 Hz and 2000 Hz bands. This average protective surfaces include: thin impervious is expressed to the nearest multiple of 0.05. membranes of or other material; perforated facings of metal, plastic or other Reflection can occur when a wave impinges material; fine wire-mesh screens; spayed-on on a boundary between two media with materials such as neoprene, and thin porous different wave propagation speeds. Some of surfaces [3]. An egg carton is a carton the incident energy (Ei) of the wave is designed for carrying and transporting reflected back into the original medium, whole , no for acoustic. These cartons and some of the energy is transmitted (Et) have a dimpled form in which each dimple and refracted (Er) into the second medium accommodates an individual egg and (See Fig. 1). This means that the wave isolates that egg from eggs in adjacent incident on a boundary can generate two dimples. This structure helps protect eggs waves: a reflected wave and a transmitted against stresses exerted during wave, whose direction of propagation is transportation and storage by absorbing a determined by Snell’s law. lot of shock and limiting the incidents of fracture to the fragile egg shells. An egg 2. Measurement Methodology carton can be made of various materials, At a given frequency, the absorption including Styrofoam, clear plastic or may coefficient of any material varies with the be manufactured from recycled paper and angle of incidence of the sound waves. In a by means of a mechanized room, sound waves strikes materials at Papier-mâché process. An “egg crate many different angles. For this reason, mattress”, while following a similar form, published coefficients of commercial is not used for egg transport. It is a light materials are generally measured in a weight camping mattress which makes use laboratory reverberation room in which of the dimpled structure to distribute and sound waves are nearly diffuse, so that they cushion human weight. This foam structure strike the test sample from many directions. is also occasionally used in packaging to dampen impact of sensitive material during A tone burst is a short signal used in travel. acoustical measurements to make possible differentiating desired signals from spurious reflections. The American Society

for Testing and Materials (ASTM) has developed this method; in Acoustics the

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technique is applicable in many areas such lowest frequency. Setting Equations (2) and as measurement of distortion, early (3) equal we obtain the optimum pulse reflections, absorption, and phase response length and corresponding transducer [5]. In our experiment the tone burst was spacing: hct222− generated with the Spectral Lab software ct = 2ct and the loudspeaker is a E-MU's PM5 Precision Monitor. 3hh t == One of the basic problems in room acoustic 3c 595 (4) measurements has always been to determine the direction of a certain The reciprocal of which gives the lower

reflection, and more important, its frequency limit fmin frequency content. For example, ¿what is 595 (5) the acoustic influence of an eggs carton in fmin = h an enclosed space? At the distance between transducers of The simple implementation of the Tone ⎛⎞3h (6) dctc==⎜⎟ =0.577h Burst measurement procedure, as described ⎝⎠3c in [5], is:

1. Place the loudspeaker and measuring which is the optimum spacing between microphone (B&K Type 2250) along the transducers for a given minimum room longest axis of the room. Center the dimension h. microphone/loudspeaker combination with respect to all three axes of the room. For reflections from the end walls of the Assume a room (see Fig. 3.) with the room along its longest dimension (L), the transducers equally spaced between floor length of the pulse must be shorter than the and ceiling (h, the height of the room is difference between the time it takes for the assumed the smallest of the room's first reflection to return to the microphone dimensions). First, we will only consider (L/c) and the time it takes for the direct reflections from side walls, ceiling and sound to reach the microphone (d/c). floor. The pulse length (t) must then be Ld− Hence tdLc≤ ≅<− t(7) shorter than the difference between the time c it takes to travel the reflected (2l/c) and the direct path (d/c). Hence Now reflections from the far wall only 2ld−+− h22 d d t ≤= (1) become a limitation when the minimum cc distance of Equation (7) is equal to, or less

than that of Equation (3). Setting the two hct222− d = (2) equal L= 2ct (8) 2ct The criterion that the microphone should be and substituting t from Equation (4) we get at least one wavelength from the 2 L= 3h=1.15h (9) loudspeaker gives 3 Hence the length of the room must be at d ≥ ct (3) least 15% longer than the smallest where t is the period at the lowest dimension in order for Equations 4-6 to be frequency which also corresponds to the valid. pulse length. It contains one period at the

ISSN: 1790-5095 26 ISBN: 978-960-474-192-2 RECENT ADVANCES in ACOUSTICS & MUSIC

However, with reflections from the end measurements. Certain standards, of course, walls setting the limits, the pulse length also call for fixed distances. must be (from Equation 8.) 3. At a given angle between the L L t == (10) loudspeaker and the barrier, we set a 2688c distance d/2 between the loudspeaker and with an optimum distance between the B&K type 2250. Note that the total transducers (combining Equations 3. and 8.) distance for the wave is d, see fig. 6. The L (11) short tone burst is emitted again and the d = 2 B&K type 2250 receives the direct and reflected signals, see fig 5. Note the point of the first reflections and increase the B&K Tone duration of the tone burst. If the tone burst Burst Type h/2 is too long, the received signal will have 2250 overlaps. h d/2 d/2 Loudspeaker h/2 Direct Reflection (L-d)/2 (L-d)/2

L

Reflection Fig. 3. The geometry environment

Direct 2. Begin with a relatively short tone burst

about 3 ms at the wished frequency and observe the received waveform on the B&K Fig. 5. The Direct and Reflect Sound Type 2250. See Fig. 4. 4. With direct and reflected signals, the

Sound Power Level (Lw) is calculated and compared for a same way: incident angle and frequency, in octave bands. Sound intensity may be used when measuring sound absorption in situ.

Tone Burst Loudspeaker Barrier B&K Figure 4. Emitted Tone Burst and Type Received Signal 2250

d/2 φ° d/2 At the same time, the size of the loudspeaker must be considered in Sample determining the far field. The microphone should be placed at a distance at least equal to the largest dimension of the loudspeaker. Fig. 6. The geometry environment Unfortunately, due to practical restrictions with angles on room size, these criteria are often ignored, thus leading to non reproducible

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A tone burst contains not only the For example for a frequency of 2 KHz with frequency of the sine wave contained in the an angle of 45°, the power W measurement burst but also a band of harmonic in the B&K type 2250 was 3.16 watts, can frequencies originated by the sine wave be corroborated with the Power Spectral frequency. These frequencies arise due to Density of the signal the square wave by which the sine signal is gated. (16)

Advantages: It is not necessary to have a We can use the following data: the reverberation chamber to accomplish the reflection factor R=0.31 (Equations 12. and test; samples of different material can be 13.), the specific impedance ζ=2.68 measured in situ with different angles. (Equation 15.), the absorption coefficient α=1-0.31=0.69 (Equation 14.) and the Disadvantage: The tone Burst Method is NRC= 0.4725. truly effective beginning at 1000 Hz, consequently it is somewhat limited to test The absorption coefficients measured in low frequencies. octave bands are:

3. Experiment and Results Hz αθ 125 0.04 The sound power level of a source in 250 0.30 500 0.42 decibels, is given by 1000 0.48 W 2000 0.69 Ldw =10log 10 ( ) B (12) W0 4000 0.69 Where W is the power of the source in watts

and W0 is the reference power in watts. Table 1. Absorption coefficients in octave The reflection factor R is related to the wall bands. impedance Z by:

P Z cos ϑ − Z (13) R ==r 0 P ZZcosϑ + i 0

Zo=ρoc is the characteristic impedance of air. The wall impedance Z is defined as the ratio of sound pressure to the normal Fig. 7. Absorption coefficients in octave component of particle velocity, both bands determined at the wall [1]. This method was corroborated using the The absorption coefficient, is given by Bell Acoustic Panel and the result was ρρ22− similar to the technical specifications of the α ==− ir 1 R 2 (14) 2 material (α= 0.75) for the data shown in the ρi example. And the specific impedance 4. Conclusions 11+ R ξ = (15) cosϑ 1− R The egg carton has a good absorption coefficient from 2 KHz on. For frequencies lower than 2 KHz it has poor absorption

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properties. It is important to point out that the test has no significance below 1 KHz, but the absorption measured at that frequency is bad enough to disregard this material.

Along with it, the egg carton does not have reflection properties, so it cannot be used for acoustic purposes.

5. References

[1] Michael Vorländer, Auralization, RWTH First Edition (Springer 2008).

[2] Cyril M. Harris, Handbook of Acoustical Measurements and Noise Control, 3 Edt. (Acoustical Society of America 1998)

[3] Thomas D. Rossing Edition, Springer handbook Acoustic, (Springer 2007).

[4] http://en.wikipedia.org/wiki/Egg_carton.

[5] MФller Henning and Thomsen Carsten, Electro Acoustic free field measurements in ordinary rooms using gating techniques, Brüel & Kjaer, (Applications notes 1975)

In memory of Eng. Fernando von Reichenbach.

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