ljud i byggnad och samhälle (vtaf01) sound propagation ... · m. barbagallo, d. bard / ljud i...

Ljud i byggnad och samhälle

(VTAF01) – Sound propagation outdoors

MATHIAS BARBAGALLODIVISION OF ENGINEERING ACOUSTICS, LUND UNIVERSITY

M. Barbagallo, D. Bard / Ljud i byggnad och samhälle / VTAF01 / 9 April 2019

… 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)

Source Conveying medium Receptor

• Sound pressure level (SPL / Lp)

Lp = 10 logp2

pref2 = 20 log

p

pref

p = p f ≡ RMS pressurepref = 2·10−5 Pa = 20 μPapatm = 101 300 Paptot(t) = patm ± p(t)


Outline

Introduction

Types of propagation

Outdoor propagation

Obstacles

Summation of sources

Summary


How does sound propagate?

Source Propagation Receiver


Definitions (http://www.acoustic-glossary.co.uk)

• 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 ∞


Definitions (http://www.acoustic-glossary.co.uk)

• 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 free-

field 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.


Free field


Diffuse field


Sound (acoustic) intensity – definition

• Sound power (i.e. rate of energy) per unit area [W/m2]

‒ Instantaneous value:

‒ Vector quantity: energy flow and direction:

– In a free field (plane waves):

• In decibels…

ԦI = pv =1

Tන

0

T

p t v t dt

I =෪p2

ρc; I ∝ p2

NOTE 1: I is the magnitude of the time average ԦI

LI = 10 logI

Iref; Iref = 10−12 ൗW m2

ԦI t = p(t)v(t)

NOTE 3: Free field occurs when the sound field is not influenced by any surrounding object or close surfaces

NOTE 2: p t is the particle pressure and v t the particle velocity

NOTE 4: In a perfectly diffuse sound field the sound intensity is zero


Sound (acoustic) power – definition

• Rate of energy transported through a surface [W=J/s]

‒ Scalar quantity

– Instantaneous value:

– Time average:

• In decibels…

W t = න

S

ԦI x, t ∙ ndS = න

S

In x, t dS

W =1

Tන

0

T

W t dt

LW = 10 logW

Wref; Wref = 10−12W

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).


(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/m3 = Pa∙s/m = Rayl]

− 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]

− Scalar quantity

z =p

u=

p

uei(φp−φu)= ρc

𝑍 =𝑧

𝐴


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/m2]


Do not mix up concepts (II)…

• Zero levels…

− SPL:

▪ Threshold of hearing: p0=20 μPa Lp(f = 1 kHz)=0 dB

− SIL:

▪ Threshold of hearing: I0=1·10−12 W/m2 LI(f = 1 kHz)=0 dB

Amplitudes are the same / Directions are the

difference (easier to troubleshot with SI)


Do not mix up concepts (III)…


Outline

Introduction


Outdoor propagation

Obstacles


Summary


Sound propagation – distance

• Pressure as function of time and position: p(x,t)

• Plate sending out sound through a tube (no losses): plane propagation

kxtieptxp ˆ),(


• Plane:

• Cylindrical:

• Spherical:


I r ∝1

r2;

I ≡ constant ;

I(r) =∏

4πr2

I r ∝1

r; I(r) =

∏

2πhr


Distance laws

• Spherical propagation

(point source)

• Cylindrical propagation

(line source)

• Plane wave

1

212 log20)()(

r

rrLrLL

1

212 log10)()(

r

rrLrLL

0)()( 12 rLrLL

0)()2( 11 rLrLL

dB6)()2( 11 rLrLL

dB3)()2( 11 rLrLL

Doubling the distance…




Do not mix up concepts (IV)…

Source: http://www.sengpielaudio.com/calculator-distance.htm


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?


Notes (I)

• Sound emission

− Sound power continuously emitted from a sound source

• Sound power level (SWL / LW / 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: 10-12 W)

LW = Lp + 10 logQ

4πr2

• Q=1: Full sphere

• Q=2: Half sphere

• Q=3: Quarter sphere

• Q=4: Eighth sphere Source: www.sengpielaudio.com


Notes (II)

• Sound pressure level (SPL / LP)

− Sound field quantity

− Relation between sound pressure and distance from source:

− 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 / LI)

− Sound energy quantity

− Relation between sound intensity and sound pressure:

− Decreases by (−)6 dB for doubling of the distance from the source to 1/4 (25%) of the

sound intensity initial value (spherical propagation)

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 ∝ p2

p ∝1

r

Lp,2 = Lp,1 + 20 logr1r2

LI,2 = LI,1 + 10 logr12

r22


Outline

Introduction


Outdoor propagation

Obstacles


Summary



Outdoor sound propagation (spherical) (I)

In real atmosphere, conditions deviate from spherical due to e.g. absorption of

sound in air, metheorological conditions, interaction with ground and obstacles...

11)log(204

log10)log(20log1000

2

0

rDIL

cW

prQLL wwp

Directivity index (DI)

Under typical weather conditions

Eabswp AArDILL 11)log(20 miscbarriervegetationturbulencegroundweatherE AAAAAAA

Atmospheric or air

absorption [dB]

Aabs=𝛾[dB/km]ᐧrWind, temperature

Geometrical divergence

(distance –r- reduction)


Outdoor sound propagation (II)

Factors influencing the sound propagation outdoors

1. Weather and wind

2. Obstruction (hindering) objects

3. Reflection



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

Shaded area

Source


Outdoor sound propagation – Temperature (I)

• Sound propagation speed:

‒ In a cold winter night, the sound is heard ”slower” than in a summerday

Temperature

Shaded area

Source

Temperature

Source

a)

b)

2732

][14.331

2732

][1

)0(

0 CTCT

T

Pc airair

air

air


Outdoor sound propagation – Temperature (II)

Source: http://www.schoolphysics.co.uk


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 = 1 - 0.05y)

Propagation of a spherical wave:

wave speed in the x-direction is

constant, whereas in the vertical

y-direction increases with height

(c = 1 + 0.05y)


Outdoor sound propagation – Temperature (IV)

• Snell’s law

- Speed of propagation varies

- Frequency remains constant


Doppler effect (I)

• Change in frequency or wavelength of a wave (or other periodic

event) for an observer moving relative to its source


Doppler effect (II)

• Example: video

https://www.youtube.com/watch?v=h4OnBYrbCjY


Regulations – Industry noise (I)

• Naturvårdsverket om buller från industrier


Regulations – wind turbine noise

• By the façade

CaseMeasur

eValue

Normal LAeq,24h 40 dBA

Low background noise LAeq,24h 35 dBA

If the sound contains audible tones -5 dB more

NOTE: regulations regarding traffic noise in the next lecture


Outline

Introduction


Outdoor propagation

Obstacles


Summary


Diffraction – Sound ”bending” (I)

• Om d > the obstacle ”exists”

• Om d < the sound bends around the obstacle

Shadow d

a)

b) No shadow


Diffraction – Slit

• Opening << : spherical wave after the obstacle (slit)

• Opening >> : plane wave after the obstacle (slit)

Wave


Example – Tsunami


Noise barriers

• << H

• >> H

Shadow

H

Screen

MORE ABOUT THIS IN THE TRAFFIC NOISE LECTURE


Outline

Introduction


Outdoor propagation

Obstacles


Summary


Summation of noise (I)

• Types of sources

‒ Correlated (or coherent)

» Constant phase difference, same frequency

» Interferences (constructive/destructive)

‒ Uncorrelated (or uncoherent)

» Different frequencies/sources

The total RMS pressure:

Lp,tot = 20 log

n=1

N

10Lp,n20

Lp,tot = 10 log

n=1

N

10Lp,n10

For uncorrelated

sources, the 3rd term

vanishes

ptot2 = p1

2 +p22+

2

∆tන

t0

t0+∆t

p1 t p2 t dt


Summation of noise (II)

• Graphical methods

‒ Adding equally loud incoherent sources

‒ Adding two different sources

» e.g. L1=61 dB / L2=55 dB

‒ Substracting two different sources

» e.g. LS+N=65 dB / LN=60 dB

Lt= 62 dB

Lt= 63.4 dB


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.

kxti

kxti

eptxp

eptxp

22

11

ˆ),(

ˆ),(

NOTE: Uncorrelated addition:

• Two sources in phase:

• Two sources in counter phase:

)()( 21 tptp

2

1

2 ~4~ pptot dB64log10 1,1,, pptotp LLL

)()( 21 tptp 0totp


Measurement by a façade

• Sound interferes with his own reflection!


Outline

Introduction


Outdoor propagation

Obstacles


Summary


Summary

• Types of propagation

‒ Plane

‒ Cylindrical

‒ Spherical

• Outdoor propagation

• Wave obstacles

• Summation of sources

‒ Correlated

‒ Uncorrelated

Thank you for your attention!

[email protected]

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