Building Acoustics

268 Building acoustics

inside a subsystem. Implicitly; all quantities E, n and W are functions of frequency and

generally we shall use the angular frequency ω in the equations.

A simple practical example is depicted in Figure 7.3, a freely suspended plate

forced into vibrations by the sound field set up in the room by a loudspeaker. In section

7.3.1 below we shall apply the equations, which follow from the assumptions above, to

calculate the amount of vibration resulting from a given input power to the room.

1 2

diss

W 1

diss

W 2

in

W 1

in

W 2

'

W 12

'

W 21

1 2

diss

W 1

diss

W 2

in

W 1

in

W 2

'

W 12

'

W 21

E 11 n E 22 n

Figure 7.2 System with two components (subsystems).

W

V

S

Figure 7.3 Example of a system with two components; a room being the acoustic component having volume V
and a free hanging panel of area S as the solid structure.

Assumption no. 1 above gives

WaEdiss= ⋅ , (7.1)

where a is factor of proportionality. As shown earlier (see section 6.4.1), we found for a
plate, having an area S and a mass m per unit area, that the relationship between the its
mean square velocity and mechanical power W was given by

WmS u^2 E,
ω

ωη ωη

Δ

=⋅ = (7.2)