Sound propagation outdoors - ISI · PDF fileSound propagation outdoors Fundamental equation directivity of the source geometrical spreading atmospheric absorption ground e ect vegetation

Sound propagationoutdoors

Fundamentalequation

directivity of the source

geometrical spreading

atmospheric absorption

ground effect

vegetation

obstacles

reflections

meteorologicaleffects

mechanisms

calculation methods

back

Acoustics I:sound propagation outdoors

Kurt Heutschi2013-01-25


Fundamentalequation




ground effect

vegetation

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reflections


mechanisms

calculation methods

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fundamental equation forpoint-to-point propagation


Fundamentalequation




ground effect

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fundamental equation according to ISO

9613-2

Lp(receiver) = LW + D −∑

A

I Lp: sound pressure level at the receiver

I LW : sound power level of the source

I D: possible correction for a directivity of the source

I A: attenuation terms describing propagationI attenuation terms A are typically frequency

dependent → calculation in frequency bands(third-octaves or octaves)


Fundamentalequation




ground effect

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Fundamentalequation




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directivity corrections D for an omnidirectional pointsource in different arrangements:

source configuration radiationinto solidangle

D[dB]

open space 4π 0in front of a surface 2π +3in front of two orthogo-nal surfaces

π +6

in front of a corner π2

+9


Fundamentalequation




ground effect

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attenuation:geometrical spreading


Fundamentalequation




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attenuation: geometrical spreading

I reduction of sound pressure with increasing distancedue to the distribution of the sound power over anincreasing area

I frequency independent

relation for a point source:

I =W

4πd2

whereI : intensity at distance d from the sourceW : sound power of the source


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attenuation: geometrical spreading

for distances larger than a few wave lengths holds:

I =p2

ρ0c→ p2 =

W ρ0c

4πd2

p2

p20

=W

W0· 1

d2· W0ρ0c

4πp20

Adiv = 20 log

(d

d0

)+ 11 [dB]

whered : distance source - receiverd0: reference distance = 1 m


Fundamentalequation




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attenuation:atmospheric absorption


Fundamentalequation




ground effect

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attenuation: atmospheric absorption

I conversion of sound energy into heat

I constant fraction of absorbed energy per unitdistance

I depends strongly on frequency

I depends on temperature and humidity


Fundamentalequation




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attenuation: atmospheric absorption

Aatm = αd [dB]

α in [dB/km]:

T[C] F[%] 125 250 500 1k 2k 4k 8k10 70 0.4 1.0 1.9 3.7 9.7 33 11720 70 0.3 1.1 2.8 5.0 9.0 23 7715 50 0.5 1.2 2.2 4.2 11 36 12915 80 0.3 1.1 2.4 4.1 8.3 24 83


Fundamentalequation




ground effect

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attenuation?:ground effect


Fundamentalequation




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attenuation?: ground effect

experiment:

auralization:

I noise in 50 m at 3m, 1m, 0.4m, 0.2m, 0.0m

I noise in 100 m at 3m, 1m, 0.4m, 0.2m, 0.0m


Fundamentalequation




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experiment: spectra of the microphone signals

50 m 100 m

3 m

0.4 m

0.0 m


Fundamentalequation




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I sound propagation close to the ground →significant ground reflection

I constructive and destructive interference with thedirect sound


Fundamentalequation




ground effect

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attenuation?: ground effectempirical approximation according to ISO 9613-2:

Aground = 4.8− 2hmd

(17 +

300

d

)≥ 0 [dB(A)]

wherehm: average height above ground of the direct soundpropagation path [m]d : distance source - receiver [m]

DΩ = 10 log

(1 +

d2p + (hs − hr)

2

d2p + (hs + hr)2

)wherehs : height of the source above ground [m]hr : height of the receiver above ground [m]dp: horizontal source-receiver distance [m]


Fundamentalequation




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attenuation?: Ground effect

today available:

I ”exact” numerical solution of the interference effectbetween direct and ground reflected sound for apoint source above flat and homogeneous ground

I → groundf.exe


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attenuation:vegetation


Fundamentalequation




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attenuation: vegetation

relevant attenuation due to vegetation only for depths >10 mAfoliage :

depth 250 500 1k 2k10. . .20m 1dB 1dB 1dB 1dB20. . .200m 0.04dB/m 0.05dB/m 0.06dB/m 0.08dB/m> 200m 8dB 10dB 12dB 16dB


Fundamentalequation




ground effect

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attenuation:obstacles


Fundamentalequation




ground effect

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attenuation: obstacles - noise barriers

I noise barriers with specific mass > 10 kg/m2

I acoustically relevant if sightline between source andreceiver is interrupted


Fundamentalequation




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barrier attenuation given by effect of diffraction:


Fundamentalequation




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I attenuation is mainly influenced by the path lengthdifference (in wave lengths) introduced by theobstacle

I increasing attenuation with frequency

path length difference:

large small large


Fundamentalequation




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calculation:

Ascreen = 10 log

(3 +

C2

λC3zKw

)[dB]

whereC2 = 20C3 = 1 for single barriersλ: wavelengthz : path length differenceKw : meteo-correction factor ≤ 1.0


Fundamentalequation




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calculation with a wave theoretical model:

500 Hz 2 kHz


Fundamentalequation




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amplification:reflections


Fundamentalequation




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amplification: reflections

2 type of reflections:

I specular reflectionI large and smooth surfaces

I diffuse reflectionI surfaces that are significantly structured in depth

(measured in wave lengths)I surfaces with inhomogeneous surface properties

(impedance)


Fundamentalequation




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amplification: reflections: specular

specular reflection:

I e.g. at a smooth facade or noise barrier

I mathematical treatment with mirror source →energetic superposition

I check, whether point of reflection is on the reflector→ yes/no

I possible attenuation by absorption

I possible attenuation due to insufficient surfaceextension (check with Fresnel zone)


Fundamentalequation




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amplification: reflections: diffuse

diffuse reflections:

I e.g. at structures facades, at forest rims, at rocks, ...

I mathematical treatment more difficult than mirrorsource concept for specular reflection

I models based on energy conservationI often Lambert directivity assumed


Fundamentalequation




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amplification: reflections: diffuse

example: reflection of a shot at a forest rim:


Fundamentalequation




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meteorological effectson sound propagation


Fundamentalequation




ground effect

vegetation

obstacles

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mechanisms

calculation methods

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mechanisms


Fundamentalequation




ground effect

vegetation

obstacles

reflections


mechanisms

calculation methods

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meteorological influences on sound

propagation

relevant meteorological parameters:

I temperature and humidity

I vertical gradients of temperature

I vertical gradient of wind speed

I inhomogeneities and turbulences


Fundamentalequation




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mechanisms

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consequences oftemperature and humidityvariations on atmospheric

absorption


Fundamentalequation




ground effect

vegetation

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mechanisms

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consequences of temperature and humidity

variations on atmospheric absorption

I dependency of atmospheric absorption on thecondition of the atmosphere:

I humidityI temperature

I calculation with formulas in ISO 9613-1

I average values for CH: humidity: 76%, temperature:8C


Fundamentalequation




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consequences oftemperature gradients


Fundamentalequation




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consequences of temperature gradients

temperature dependency of sound speed:

c ≈ 343.2

√T

293

c : sound speed in [m/s]T : air temperature in Kelvin

typical +0.6 m/s per degree C


Fundamentalequation




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consequences of temperature gradients

tilting of plane wave fronts:

decreasing temp. with height increasing temp. withheight


Fundamentalequation




ground effect

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consequences of wind


Fundamentalequation




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I stepwise construction of wave fronts in a movingmedium

I given: wave front at time t0

I wanted: wave front at time t1


Fundamentalequation




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I wind means always a vertical gradient

I sound propagation speed becomes height dependent

I curved propagation analogous to case oftemperature gradients

upwind downwind


Fundamentalequation




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examples of wind and temperature profiles

u(z) = uref

(z

zref

)0.15

T (z) = T (0) + kz0.2

(1)


Fundamentalequation




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consequences of curvedpropagation


Fundamentalequation




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consequences of curved propagation

I upwards curvature: development of shadow zones →high attenuation

I downwards curvature: sound wave may rise abovebarriers, ground effect is lowered → amplifyingeffect


Fundamentalequation




ground effect

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mechanisms

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consequences of turbulences


Fundamentalequation




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consequences of turbulences

consequences at a receiver point:

I temporary level fluctuations (≈ energy neutral)

I scattering of sound energy into shadow zones

I coherence loss between different propagation paths


Fundamentalequation




ground effect

vegetation

obstacles

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mechanisms

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methods to calculatemeteorological

effects on sound propagation


Fundamentalequation




ground effect

vegetation

obstacles

reflections


mechanisms

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methods to calculate meteorological

effects on sound propagation

I empirical approaches regarding barrier attenuation(ISO 9613-2)

I analytical geometrical approach to handle curvedpropagation: description with circles

I numerical geometrical approach to handle curvedpropagation: ray tracing

I numerical solutions of the wave equation:I Parabolic Equation (PE)I Finite Differences in the Time Domain (FDTD)


Fundamentalequation




ground effect

vegetation

obstacles

reflections


mechanisms

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empirical approaches forthe barrier attenuation


Fundamentalequation




ground effect

vegetation

obstacles

reflections


mechanisms

calculation methods

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empirical approaches for the barrier

attenuation

calculation of the barrier attenuation according to ISO9613-2:

Dz = 10 log

(3 +

C2

λzKmet

)≤ 20.0 bzw. 25.0

whereC2 = 20 respectively 40z : path length difference [m]

Kmet = exp(− 1

2000

√dssdsrd

2z

)< 1.0

dss : distance source - barrier [m]dsr : distance barrier - receiver [m]d : distance source - receiver [m]


Fundamentalequation




ground effect

vegetation

obstacles

reflections


mechanisms

calculation methods

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analytical geometricalapproach:

description with circles


Fundamentalequation




ground effect

vegetation

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mechanisms

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analytical geometrical approach:

description with circles

I necessary assumption: linear vertical profile of thesound propagation speed → constant gradients →curvature along circles

I curvature (radius) can be determined analytically

I with help of the circles calculation of modifiedbarrier attenuation and altered ground effect


Fundamentalequation




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calculation of the radius of the circle

radius depends on

I sound propagation speed at height of the sourcec(z)

I gradient of the sound propagation speed with heightdcdz

I elevation angle of emission θI for θ = 0 and dc

dz ≈ ± 0.05 [s−1], R ≈ a fewkilometers

caution: the fundamental assumption of constantgradients is problematic!


Fundamentalequation




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numerical geometricalapproach:ray tracing


Fundamentalequation




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ray tracing

I sound ray: curve in space that describes thepropagation of a point of a wave front

I numerical procedure for a stepwise construction

I arbitrary wind and sound speed gradients can beconsidered


Fundamentalequation




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ray tracing


Fundamentalequation




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ray tracing

evaluation of the ray tracing process for propagationattenuation calculations:

1. search of all rays that connect source and receiver

2. determination of sound pressure at the receiver bysummation of all rays


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ray tracing

I advantages:I relatively fast algorithmI empirically extendable for further effects such as

reflections

I difficulties:I singularitiesI as it is a geometrical approach, wave phenomena

are ignoredI very sharp but unrealistic transitions (shadow

zones)I empirical extensions necessary to handle barriers


Fundamentalequation




ground effect

vegetation

obstacles

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mechanisms

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numerical solutions of thewave equation:

parabolic Equation


Fundamentalequation




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parabolic equation, PE

I originally developed in underwater acoustics, since30 years in use for outdoor sound

I formulation in the frequency domain (Helmholtzeq.: 4p + ω2

c2 p = 0)

I Helmholtz equation in cylindrical coordinates foraxial-symmetrical approximation (2D calculation forpoint source behavior)

I separation of the sound field into a slowly varyingamplitude information and an oscillation term

I simulation region: 2D grid with mesh size ≈ 0.1λhorizontal, resp. ≈ 10λ vertical


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parabolic equation, PEI advantage compared to FE: stepwise solution

p(r , z)→ p(r + ∆r , z) ⇒ only systems of equationwith M variables have to be solved(M : number ofelements in height)


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parabolic equation, PE

difficulties:

I originally only applicable for flat ground

I however, approximations for undulating groundpossible

I abrupt changes in topography (e.g. barriers) arecritical

I high computational effort


Fundamentalequation




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mechanisms

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numerical solution of thewave equation:

finite differences in the timedomain (FDTD)


Fundamentalequation




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finite differences in the time domain

(FDTD)

I basic equations:I grad(p) = −ρ∂~v∂tI −∂p

∂t = κP0div(~v)

I simulation region: 2/3D grid with mesh size ≈ 0.1λ

I calculation by step-wise updating of the sound fieldvariables

I advantage:I no system of equations has to be solvedI result is an impulse response (containing all

frequencies)


Fundamentalequation




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(FDTD)

vnewx = v old

x − α (pright − pleft)

pnew = pold − β (vxright − vx left)− β (vytop − vybottom)


Fundamentalequation




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(FDTD)

difficulties:

I approximation of ground impedance in the timedomain is delicate

I high computational effort


Fundamentalequation




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input parameters?


Fundamentalequation




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input parameters?

I meteorological effects for sound propagation can becalculated today

I but: who can deliver the necessary input data (windspeed, temperature in necessary spacial resolution))

I modern meteorological models reach very fineresolutions (example. COSMO2 Meteo Schweiz, 2.1km mesh size)


Fundamentalequation




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Example: COSMO2 evaluation of

probability of near ground inversion


Fundamentalequation




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eth-acoustics-1

Documents

Sound propagation outdoors - ISI · PDF fileSound propagation outdoors Fundamental equation directivity of the source geometrical spreading atmospheric absorption ground e ect vegetation