Sound Propagation

2003 Annual Sales Meeting

Copyright Nelson Acoustical Engineering & JGS Consulting

Sound Propagation



r

Sound Propagation – Free Space

Free Space

P

Basic Relationship

Lp(r) = Lw – 20 log r – C

SourceLW

C=0.6 dB if r is in feet;C=10.9 dB if r is in meters

Sound Pressure Level inversely proportional to distance (r)

squared. 20*log r = 6 dB/double distance

Another Useful FormLp(r) = Lp(r0) – 20 Log (r/r0)

Energy is spread over larger area as sound propagates, causing sound pressure level to decrease with distance from source



P

Sound Pressure Level in Enclosed Space

“Near” SourceSound Power Level

of Source is dominant factor in determining Sound Pressure Level in

“Direct Field”

“Far” From SourceBoth Sound Power Level of Source and

Acoustical Properties of

Enclosed Space are factors in

determining Sound Pressure Level in

“Reverberant Field”

Sound Pressure Level

Distance

Direct Field

Reverberant Field



Sound Pressure Level in Enclosed Space

Sound Pressure Level

Distance

Near SourceSound Power of Source is dominant factor in determining sound pressure level.Sound pressure level decays at 6 dB/doubling of distance.

Direct Field.

Far from SourceSound Pressure Level is constant and determined by Sound Power of Source AND Room Constant.Reverberant Field.

In BetweenSound Pressure level decreases as less than 6 dB/doubling of distance until Reverberant Field dominates.

Reverberant Environment



Sound Pressure vs. Sound Powerin an enclosed space

R=3

R=10

R=30

R=100

R= infinite

Q=2

0.1 1.0 10.0Distance [m]

-30

-20

-10

0

10

20

Lp -

Lw

[dB

]Small

Reverberant Spaces

Anechoic Spaces

Assumptions:1. Reverberant sound field

is diffuse = high mode count

Room Dimensions>>λ

Large Reverberant

Spaces

Room Constant (R)

αα−

=1SR

α = average sound absorption coefficient of the enclosure surfaces



Acoustic Properties of Enclosed Spaces are Frequency Dependent

R=3

R=10

R=30

R=100

R= infinite

Q=2

0.1 1.0 10.0Distance [m]

-30

-20

-10

0

10

20

Lp -

Lw

[dB

]

High Frequencies>500 Hz

Large Room Constant

Low Frequencies<500 Hz

Smaller Room Constant

If you are measuring at 2

meters, this would be your “error” at low frequencies



General Relationship between Sound Pressure and Sound Power Levels in Large Rooms

CRr

QLrL wp +⎟⎠⎞

⎜⎝⎛ +

Π+=

44

log*10)( 2θ

Lp(r) = Sound Pressure Level at distance r from source (in dB re 2 x 10-5 Pa)

Lw = Sound Power Level of source (in dB re 1x10-12 watts)

Qθ = directivity factor of source in direction θ

R = Room Constant (in ft2 or m2; see C) αα−

=1SR

α = average sound absorption coefficient of enclosure surfaces (dimensionless)

C = Constant (0 if r is in meters and α in m2; 10 dB if r is in ft and α in ft2



Observations from the General Relationship between Sound Pressure and Sound Power Levels

in Large Rooms

CRr

QLrL wp +⎟⎠⎞

⎜⎝⎛ +Π

+=4

4log*10)( 2

θ

This term is related to how big the room is.

Note that it increases as the DISTANCE SQUARED

This term is related to the absorptive properties of

the room walls

Note that it is linearly related to the absorption

For Anechoic Chamber, the size of the chamber is more important than the absorptive properties of the wall treatment. BIG CHAMBERS WORK BEST!

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Sound Propagation