2021.03.22

Acoustics VTAF 01 1.Course info & Intro to

NIKOLAS VARDAXIS DIVISION OF ENGINEERING ACOUSTICS, LUND UNIVERSITY Outline

Course Information

Introduction to Acoustics

Summary Instructors

• Lectures ‒ Delphine Bard, [email protected] ‒ Nikolas Vardaxis [email protected] [contact person] à Division of Engineering Acoustics, V-building (5th floor).

• Exercises, laboratories, project ‒ Nikolas Vardaxis

• Guest lectures – … • Administration – Birgitta Rydh, [email protected] – Cecilia Sandstedt, [email protected] My profile

• Nikolaos Georgios Vardaxis – Diploma Architectural Engineering (D.U.Th., GR) – M.Sc. and Vibration (Chalmers, SE) – Ph.D. Engineering Acoustics (LTH, Lund University, SE) – Post-doc researcher in Acoustics >>

– Research: building acoustics, room acoustics, environmental , human perception, data analysis.

– Freelance: Studio and room acoustics design, production, sound design. Course material

• Handed out material – Lecture notes – Exercise tasks – Laboratory instructions (2) – Project task – Formulae

• Website (course material will be uploaded here): – http://www.akustik.lth.se/utbildning/kurser/vtaf01-ljud-i-byggnad-och-samhaelle/ Literature

• Course books – E. Nilsson m.fl. Avd för Teknisk Akustik (2008) » Free PDF on our website » Available at KFS

– Building Acoustics, T.E.Vigran, CRC Press (2008)

– Extra suggestions in the course program. Laboratories & Project task

Laboratories

• Two Lab sessions (in groups of 2-3 students)

1. Recording and analysis of vibration 2. Sound insulation measurement

• 2 hours on site

– Preparation and post-processing time needed • Results presented in technical reports

– Either passed or returned for corrections

Project task

– Performed in groups of 2-3 students – Presented Wednesday, December 16th at 15:00-17:00 Examination

The final grade will be obtained as follows…

• Written exam - Online (50%) – Tuesday 31 May at 08:00-13:00 (online). – Theoretical questions and exercises – Calculator and formulae sheet – Graded: u, 3, 4, 5 • Project task (50%) – Graded: u, 3, 4, 5 • Executed laboratories with passed reports The course aims

To understand:

• Principles of sound propagation – physical behaviour

• Effects of sound on humans

• Measurements in acoustics

• Environmental noise problems

• Building acoustics

• Room acoustics V-huset

Lab Refresh maths – Logarithms (I)

• Logarithms: • Definition log x = y b = x • Properties

− Product: log x y =log(x) + log(y)

− Quotient: log x/y = log(x) − log(y)

− Power: log x = y log(x)

− Base switch: log c = 1/ log(b)

− Base change: log x = log(x)/ log(b)

− Consequences of the definition: log 1 = 0

log x = ∄ for x ≤ 0

log x = ∞ when x → ∞ Intro maths – Logarithms (II) Outline

Course Information

Introduction to Acoustics

Summary Learning outcomes

• Definition of sound • Harmonic oscillations and complex notation • Acoustic variables and levels • Addition of correlated and uncorrelated sources • Frequency domain representation What is acoustics? (I)

• From the Oxford Dictionary:

• Acoustics: part of physics studying generation, transmission, reception, absorption, reproduction and control of sound ‒ Environmental ac., building ac., room ac., psychoac., musical ac., underwater ac… What is acoustics? (II)

[Acoustics and Audio Technology, M.Kleiner, J Ross Publishing, 2012] Sound & Noise

• Sound: oscillations produced in an elastic medium by a vibratory source producing variations in the atmospheric pressure − Characteristics: » Pitch ptot (t)= patm ± p(t) » Quality »

[ https://waitbutwhy.com/2016/03/sound.html ] Sound & Noise

• Noise: random (unwanted) sound

Example of a recorded voice saying “Hallo” Voltage amplitude in volts [v] Time in seconds [s] Time & frequency domains (I)

Harmonic signal: y t = A sin ωt = A cos ωt + � = A sin 2πf t

‒ Amplitude: A T λ

‒ 1 A Period [s]: T = f 1 ‒ Frequency [Hz]: f = T

‒ Wavelength [m]: λ=cT= ⁄ FFT

‒ Propagation Speed [m/s]: c=f λ NOTE: c ≠ v

‒ Effective value (RMS):

∆ 1 A = A = y t dt , A =A ‒ Frequency domain harmonic 2 ∆t signal Complex notation

• Equivalent description: p t =A cos ωt+φ

p t =Re Ae() = Re Ae

where the complex amplitude is defined as: A = Ae and e = cos φ + i sin φ

• The peak value and initial phase are A = A Im[A] tan (φ) = Re[A]

NOTE 1: The complex number ”i” is sometimes also expressed as ”j” π NOTE 2: φ = φ − 2 Phase φ

• Phase

[Wikipedia: Phase (waves)] Equivalences

Source: Sven Spanne: Komplex Analys Different frequencies

4000 Hz 2000 Hz

1000 Hz

500 Hz Source: Ecophon 250 Hz 125 Hz 63 Hz of a tone [dB] Level Pressure Sound Sound

1000 Frequency [Hz] Spectrum of noise [dB] Level Pressure Sound Sound

Frequency [Hz] Frequency domain – Noise

• Noise: Classified by ”colours” • Violet noise: +6 dB/octave • Blue noise: +3 dB/octave • : flat spectrum • : -3 dB/octave • Brown noise: -6 dB/octave

[Wikipedia: ] Time & frequency domains (II)

• A more complex time signal (traffic load)

FFT

• Narrow band analyses ‒ Impractical, time-consuming ‒ Octave & 1/3 octave bands

NOTE: Spectrum (any magnitude plotted against frequency) Time & frequency domains (II)

Frequency responses:

Narrow band

Octave bands

1/3 octave bands

[www.comsol.com/blogs/new-octave-band-plot-for-acoustics-simulations-in-version-5-2/] Time & frequency domains (II) Audible range

• Normal vs. Impaired

O A U E Y P 35-80 dB B M R V S F T

125-8000 Hz Source: Ecophon process

• Pressure waves • For a sound to be perceived ‒ Frequency: 20 Hz – 20 kHz ‒ Sound pressure level (SPL): frequency dependent • Inner ear detects: ∆p ϵ [20 μPa, 200 Pa] à wide range ‒ Use of (in )

Source Conveying medium Receptor The (dB) & SPL

• Logarithmic way of describing a ratio ‒ Ratio: velocity, voltage, acceleration… ‒ Need of a reference

• Sound pressure level (SPL / Lp)

p p L = 10 log = 20 log p p

p = p f ≡ RMS pressure p = 2·10 Pa = 20 µPa p = 101 300 Pa p(t) = p ± p(t)

‒ p measured with microphones ‒ Frequency response of human hearing changes with amplitude Frequency weightings

• Frequency response of human hearing changes with amplitude • How to relate the objective measure to the subjective experience of sound? Frequency weightings – Examples of SPL Frequency weightings

• Filters and calculation

() L = 10 log 10 Frequency weightings (I)

• Correlate objective sound measurements with subjective human response

‒ A-weighting [dB(A)/dBA]: designed to reflect the response of how the human ear perceives noise, i.e. 20 Hz-20 kHz » Only really accurate for relatively quiet and pure tones? » Low frequency noise is suppressed (wind turbine noise?)

‒ C-weighting [dB(C)/dBC]: developed for high level aircraft noise

‒ Z-weighting: zero frequency weighting (un-weighted values)

‒ B-weighting: covers the mid-range between the A- and C-weighting

‒ D-weighting: designed for use when measuring high level aircraft noise

Fallen into disuse

______*Filters are defined in the standard IEC 61672 Frequency bands (again)

• A sound in the frequency domain may be looked at in several ways. • Narrow bands • Third-octave bands • Octave bands • Total level L Octave and 1/3-octave bands

If fn is the cut-off lower frequency and fn+1 the upper one, the ratio of the band limits is given by:

= 2

where k=1 for full octave and k=1/3 for one- third octave band

1 NOTE 1: Convert octave band to 1/3-octave band level reduction of L = 10 log 3 -4.771dB for each 1/3 octave band:

, NOTE 2: Octave band level of three 1/3-octave band levels: L = 10 log 10 Summation of noise

• Graphical methods ‒ Adding equally loud incoherent sources ‒ Adding two different sources

» e.g. L1=61 dB / L2=55 dB

, L, = 10 log 10 Lt= 62 dB

Lt= 63.4 dB ‒ Substracting two different sources

» e.g. LS+N=65 dB / LN=60 dB Summation of noise (I)

• Types of sources ‒ Correlated (or coherent) » Constant phase difference, same frequency » Interferences (constructive/destructive)

, L, = 20 log 10 ‒ Uncorrelated (or incoherent)

, L, = 10 log 10

∆ 2 The total RMS pressure: p = p +p + p t p t dt ∆� For uncorrelated sources, the 3rd term vanishes Noise metrics (I)

• Single event noise metrics:

‒ Maximum sound level (Lmax): » Accounts only for sound amplitude [dB/dBA…] ‒ Sound exposure level (SEL) & Single event noise exposure level (SENEL) » Total “noisiness” of an event. It takes duration into account » SENEL=SEL if measured for the period when the level is within 10 dB of Lmax

‒ Day and night average sound level (DNL or Lden) ‒ Community noise equivalent level (CNEL) ‒ Effective perceived noise level (EPNL) ‒ Time above threshold ‒ … Noise metrics (II)

• Cumulative exposure metrics ‒ Equivalent SPL during the measurement time T (units: dB, dBA…)

1 p(t) 1 () L, = 10log dt = 10 log 10 dt T p T

Ex: Calculate the Leq,8h that corresponds to 105 dBA for 15 min. Measurement of SPL

• Sound level meter ‒ Microphone measures acoustic levels omni-directionally ‒ Sampling: Fast (0.125 s), Slow (1 s), Peak (impulse value 35 ms) ‒ Weighting filters (A, C…) built-in

‒ Calculation of Leq,T, building acoustic indicators, traffic noise… ‒ Calibrated ‒ … more about this during the course labs Outline

Course Information

Introduction to Acoustics

Summary Summary

• Definition of sound • Harmonic oscillations and complex notation • Acoustic variables and levels • Frequency domain representation (freq. bands…) • Addition of correlated and uncorrelated sources

• Study from the literature

– T.E.Vigran, Building Acoustics - Ch. 3 ß Our main reference and a bible for acoustics engineering in the Nordic countries. Try some free mobile apps for acoustics!

• Sound level meter apps – OpeNoise » SPL, 1/3 oct. bands, Frequency Analyzer – Noise Exposure (Buller) » Representative dBA levels, Swedish Work Environment Authority

• Noise, ambient or masking sounds apps – White Noise » White, pink, blue noise, … , rain, thunder, seawaves, natural soundscapes… etc Thank you for your attention!

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