Building Acoustics

Room acoustics 125

(^2) tot 0 0 2

4

.

4

D

pWc

r A

ρ θ

π

⎛⎞

=⎜

⎝⎠

 +⎟ (4.48)

Expressed by the corresponding levels using standardized reference values for sound
pressure and sound power, we may write

(^2)

4

10 lg.

4

pW

D

LL

r A

θ

π

⎛⎞

=+⋅⎜+

⎝⎠

⎟ (4.49)

For simplicity, we have given the characteristic impedance ρ 0 c 0 the value 400 Pa⋅s/m.
The difference between the sound pressure level and the sound power level is shown in
Figure 4.9 as a function of the relative distance r/(Dθ)1/2. The parameter on the curves is
the absorption area A. The dashed curve indicates the relative level of the direct field.

Free field

0.1 1.0 10.0 100.0

Relative distance from source, r/(Dθ)1/2 (m)

-20

-15

-10

-5

0

5

10

Relative SPL,

L

• p

L

(dB)w A = 5 m

2

10

20

50

100

200

Figure 4.9 Sound pressure level as a function of relative distance from a source of sound power level LW. The
parameter is the room total absorption area A. The dashed line indicates the free field level.

The distance rH from the source, where the contributions from the direct field and
the diffuse field are equal, is called the hall radius or also room radius for the case where
the directivity factor is equal to 1.0:

0

55.26

.

H 16 16

A V

r

ππcT

== ⋅ (4.50)