Ljud i byggnad och samhälle (VTAF01) Sound propagation outdoors MATHIAS BARBAGALLO DIVISION OF ENGINEERING ACOUSTICS, LUND UNIVERSITY

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1 Ljud i byggnad och samhälle (VTAF01) Sound propagation outdoors MATHIAS BARBAGALLO DIVISION OF ENGINEERING ACOUSTICS, LUND UNIVERSITY

2 recap from last lectures Pressure waves For a sound to be perceived Frequency: 20 Hz 20 khz (for an average young healthy person) Sound pressure level (SPL): frequency dependent Inner ear detects: p ϵ [20 μpa, 200 Pa] wide range Use of logarithmic scale (in decibels) Sound pressure level (SPL / L p ) L p = 10 log p 2 2 = 20 log p ref p p ref Source Conveying medium Receptor p = p f RMS pressure p ref = Pa = 20 μpa p atm = Pa p tot (t) = p atm ± p(t)

3 Outline Introduction Types of propagation Outdoor propagation Obstacles Summation of sources Summary

4 How does sound propagate? Source Propagation Receiver

5 Definitions ( Near field: that part of a sound field, usually within about two wavelengths of a noise source, where there is no simple relationship between SPL and distance, where the sound pressure does not obey the Inverse Square Law. Far field: a region in free space, distant from a sound source, where the SPL obeys the Inverse Square Law (the SPL decreases 6 db with each doubling of distance from the source). 2 wavelengths 2 wavelengths to

6 Definitions ( Direct field: the region in which the sound measured can be attributed to the source alone without reflections. Early reflections that reach the listener within 50 ms integrate with the direct sound and can improve speech clarity. Later reflections may have a negative effect on speech clarity. Free field: a sound field region with no adjacent reflecting surfaces. In practice a freefield can be said to exist if the direct sound is 6 db or preferably 10 db greater than the reverberant or reflected sound. Diffuse field: the region in a room where the Sound Pressure Level is uniform i.e. the reflected sound dominates, as opposed to the region close to a noise source where the direct sound dominates. The same as Reverberant Field. Non-diffuse field: SPL is dependent on the position one measures, i.e. the direct sound dominates. Typical from low frequencies in a room, where modal density is low.

7 Free field

8 Diffuse field

9 Sound (acoustic) intensity definition Sound power (i.e. rate of energy) per unit area [W/m 2 ] Instantaneous value: ԦI t = p(t)v(t) Vector quantity: energy flow and direction: ԦI = pv = 1 T න 0 T p t v t dt In a free field (plane waves): I = p 2 ρc ; I p2 In decibels L I = 10 log I ; I I ref = W ref m 2 NOTE 1: I is the magnitude of the time average ԦI NOTE 2: p t is the particle pressure and v t the particle velocity NOTE 3: Free field occurs when the sound field is not influenced by any surrounding object or close surfaces NOTE 4: In a perfectly diffuse sound field the sound intensity is zero

10 Sound (acoustic) power definition Rate of energy transported through a surface [W=J/s] Scalar quantity Instantaneous value: Time average: W t = න ԦI x, t nds = න I n x, t ds S S T W = 1 T න W t dt 0 In decibels L W = 10 log W W ref ; W ref = W NOTE: the power ratios in decibels (e.g. acoustic power, intensity) are calculated as: 10 times base 10 logarithm of the ratio; whereas amplitude quantities (e.g. acceleration, pressure) in decibels are calculated as are calculated as ratio of squares (i.e. 20 times base 10 logarithm of the ratio of amplitudes).

11 (Acoustic) impedance definition Ratio between two field quantities Measures of the opposition that a system presents to the acoustic flow Specific acoustic impedance (z=pressure/velocity) is an intensive property of a medium (e.g. air or water)» Units: [N s/m 3 = Pa s/m = Rayl] z = p u = p u ei(φ p φ u ) = ρc Acoustic impedance (Z=pressure/flow) is the property of a particular geometry and medium» E.g. we can discuss for example the Z of a particular duct» Units: [Pa s m] Z = z A Scalar quantity

12 Do not mix up concepts (I) Sound Pressure (SPL), Sound Power (SWL), and Sound Intensity (SIL) acoustic quantities that can be expressed in db. They describe different aspects of sound, and the decibels for each represent different measurement quantities. - SPL: Amplitude level of sound at a specific location in space (scalar quantity) Dependent on the location and distance to the source Measured in Pascals [Pa] - SWL: Rate at which sound is emitted from an object Independent of location or distance Measured in Watts [W] - SIL: Sound power flow per unit of area Sound intensity is measured in [W/m 2 ]

13 Do not mix up concepts (II) Zero levels SPL: Threshold of hearing: p 0 =20 μpa L p (f = 1 khz)=0 db SIL: Threshold of hearing: I 0 = W/m 2 L I (f = 1 khz)=0 db Amplitudes are the same / Directions are the difference (easier to troubleshot with SI)

14 Do not mix up concepts (III)

15 Outline Introduction Types of propagation Outdoor propagation Obstacles Summation of sources Summary

16 Sound propagation distance Pressure as function of time and position: p(x,t) Plate sending out sound through a tube (no losses): plane propagation p( x, t) pe ˆ i tkx

17 Types of propagation Plane: I constant ; Cylindrical: I r 1 r ; I(r) = 2πhr Spherical: I r 1 r 2 ; I(r) = 4πr 2

18 Distance laws Spherical propagation (point source) L r L( r 2) L( r1 ) 20log r 2 1 Doubling the distance L L ( 1 2r1 ) L( r ) 6dB Cylindrical propagation (line source) L r L( r 2) L( r1 ) 10log r 2 1 Doubling the distance L L ( 1 2r1 ) L( r ) 3dB Plane wave L L( r2 ) L( r1 ) 0 Doubling the distance L L ( 1 2r1 ) L( r ) 0

19 Do not mix up concepts (IV) Source:

20 Sound (acoustic) intensity example Ex: In a rock concert, measurements are performed next to you yielding a value of 90 db. Which level will a person who is 5 times further away from the speakers perceive, assuming plave wave propagation? cylindrical wave propagation? spherical wave propagation?

21 Notes (I) Sound emission Sound power continuously emitted from a sound source Sound power level (SWL / L W / L ) or acoustic power Total sound energy emitted by a source per unit time» Constant regardless of the room» Independent of the distance from the sound source Units: Watts [W] or decibels [db] (re: W) L W = L p + 10 log Q 4πr 2 Source: Q=1: Full sphere Q=2: Half sphere Q=3: Quarter sphere Q=4: Eighth sphere

22 Notes (II) Sound pressure level (SPL / L P ) Sound field quantity Relation between sound pressure and distance from source: p 1 r Decreases by ( )6 db for doubling of the distance from the source to 1/2 (50%) of the sound pressure initial value (spherical propagation) Sound intensity level (SIL / L I ) L p,2 = L p, log r 1 r 2 Sound energy quantity Relation between sound intensity and sound pressure: NOTE: A sound source produces sound power and this generates a sound pressure fluctuation in the air. Sound power is the distance independent cause of this, whereas sound pressure is the distance-dependent effect. I p 2 Decreases by ( )6 db for doubling of the distance from the source to 1/4 (25%) of the sound intensity initial value (spherical propagation) L I,2 = L I, log r 1 2 r 2 2

23 Outline Introduction Types of propagation Outdoor propagation Obstacles Summation of sources Summary

24 Outdoor sound propagation (spherical) (I) L p L w 2 4p 10logQ 20 log( r) 10log 0 L DI 20 log( r) w 11 0cW0 Directivity index (DI) Geometrical divergence (distance r- reduction) Under typical weather conditions In real atmosphere, conditions deviate from spherical due to e.g. absorption of sound in air, metheorological conditions, interaction with ground and obstacles... L p L DI 20log( r) 11 A A AE Aweather Aground Aturbulence Avegetation Abarrier Amisc w abs E Atmospheric or air absorption [db] A abs =γ[db/km]ᐧr Wind, temperature Source Propagation Receiver

25 Outdoor sound propagation (II) Factors influencing the sound propagation outdoors 1. Weather and wind 2. Obstruction (hindering) objects 3. Reflection Source Propagation Receiver

26 Outdoor sound propagation Wind Generally greater than the temperature dependence Upwind / Downwind SPL reduction due to turbulence: 4-6 db/100m» Independent of wind direction» More obvious the greater the wind speed is Wind speed Source Shaded area

27 Outdoor sound propagation Temperature (I) Sound propagation speed: c air P 0 Tair[ C] Tair[ C] air ( T 0 ) In a cold winter night, the sound is heard slower than in a summerday a) Temperature Source b) Temperature Shaded area Source

28 Outdoor sound propagation Temperature (II) Source:

29 Outdoor sound propagation Temperature (III) Propagation of a spherical wave: wave speed in the x-direction is constant, whereas in the vertical y-direction decreases with height (c = y) Propagation of a spherical wave: wave speed in the x-direction is constant, whereas in the vertical y-direction increases with height (c = y)

30 Outdoor sound propagation Temperature (IV) Snell s law - Speed of propagation varies - Frequency remains constant

31 Doppler effect (I) Change in frequency or wavelength of a wave (or other periodic event) for an observer moving relative to its source

32 Doppler effect (II) Example: video

33 Regulations Industry noise (I) Naturvårdsverket om buller från industrier

34 Regulations Industry noise (I) Naturvårdsverket om buller från industrier

35 Regulations wind turbine noise By the façade Case Measur e Value Normal L Aeq,24h 40 dba Low background noise L Aeq,24h 35 dba If the sound contains audible tones -5 db more NOTE: regulations regarding traffic noise in the next lecture

36 Outline Introduction Types of propagation Outdoor propagation Obstacles Summation of sources Summary

37 Diffraction Sound bending (I) Om d > the obstacle exists Om d < the sound bends around the obstacle a) Shadow d b) No shadow

38 Diffraction Slit Opening << : spherical wave after the obstacle (slit) Opening >> : plane wave after the obstacle (slit) Wave

39 Example Tsunami

40 Noise barriers << H Screen Shadow H >> H MORE ABOUT THIS IN THE TRAFFIC NOISE LECTURE

41 Outline Introduction Types of propagation Outdoor propagation Obstacles Summation of sources Summary

42 Summation of noise (I) Types of sources Correlated (or coherent)» Constant phase difference, same frequency» Interferences (constructive/destructive) L p,tot = 20 log N n=1 L p,n Uncorrelated (or uncoherent)» Different frequencies/sources L p,tot = 10 log N n=1 L p,n The total RMS pressure: t 0 + t 2 p tot = p 2 1 +p t න t0 p 1 t p 2 t dt For uncorrelated sources, the 3 rd term vanishes

43 Summation of noise (II) Graphical methods Adding equally loud incoherent sources Adding two different sources» e.g. L 1 =61 db / L 2 =55 db L t = 62 db L t = 63.4 db Substracting two different sources» e.g. L S+N =65 db / L N =60 db

44 Yet another note on phase Two signals are in phase if the argument is the same 2n, i.e. the phase different between them should be = 2n. Two signals are in counter phase if the argument differs 2n, i.e. the phase different between them should be = 2n. p p 1 2 ( x, t) ( x, t) pˆ e 1 pˆ 2 i tkx e i tkx NOTE: Uncorrelated addition: Two sources in phase: p1( t) p2( t) ~ 2 ~ 2 p tot 4p Two sources in counter phase: 1 p Lp, tot Lp,1 10log 4 Lp, 1 6dB t) p ( ) 0 1( 2 t p tot

45 Measurement by a façade Sound interferes with his own reflection!

46 Outline Introduction Types of propagation Outdoor propagation Obstacles Summation of sources Summary

47 Summary Types of propagation Plane Cylindrical Spherical Outdoor propagation Wave obstacles Summation of sources Correlated Uncorrelated

48 Thank you for your attention!