Building Acoustics

Sound transmission 259

2200 00

44

,

cc

pWaF

A A

ρρ

 =⋅=⋅ (6.115)

where A is the total absorption area of the room. We further assume that, imbedded into
another wall of the room, we have a small (in relation to the wavelength) mass-controlled
piston of mass m and area S. The resulting force Fp on the piston, caused by the sound
field in the room, induces a piston velocity ups given by

(^) ps^2

11

uFp Sp2.

ωωmm

=⋅ = ⋅ (6.116)

This enables us to write

(^22)
ps 00
222

8

,

u cS

a

FAm

ρ

ω

=⋅



 (6.117)

where the angular frequency ω is understood to be the centre frequency of a band broad
enough to give diffuse field conditions.

Figure 6.32 Sketch of a room used for a thought experiment. a) A force F is driving a plate being part of a wall,
b) A monopole source drives the plate via the sound field in the room.

In the next part of the thought experiment (see Figure 6.32), we shall drive this
piston by the same point force used to drive the plate. The piston then gets a velocity u'ps,
thereby radiating a power W ́ into the room equal to the power from a piston in a baffle.
At low frequencies, the piston will act like a monopole source and the power may be
written (see sections 3.4.1 and 3.4.4)

(^) ()
22 22
00 2 00 2 00
22 ps'. 2
ck ck ck F
WQ Su S
m
ρρ ρ
ππ πω

⎛⎞

′′=⋅=⋅ =⋅⎜⎟

⎝⎠



 (6.118)

In the last expression we have inserted the relationship between the force and the
resulting velocity of the piston. This power will again set up a sound field in the room
having a sound pressure p ́ given by

p

F

F p'

a) b)

ups

up

u'ps