Building Acoustics

Multilayer elements 287

wall area S we may just multiply by n to arrive at the total radiated power. We have
assumed that the radiation factor of the basic wall is approximately equal to 1.0, hence

Wcu 1001 =U ^2 S. (8.14)

Equations (8.12) through (8.14) then give

4 1

2

iii 0 2,B

2 B

2,P 2,B 2,P 2,B (^11)

.

WWWf u

n

WW W nW Wf u

V

−

⎡⎛⎞ ⎤

==+⎢⎜⎟ ⋅⎥

++⋅'⎢⎝⎠ ⎥

⎣ ⎦





(8.15)

Wi W 1 Wi

W2,P

W2,B

u 1

u2,B

a) b)

Figure 8.8 Heavy basic wall with additional acoustical lining.

Inserting this equation into Equation (8.11), we get

1

(^42)
0 2,B
2 B
1

,

where 10 lg.

RR R

f u

Rn

f u

V

=+'

⎡⎛⎞ ⎤

'=− ⋅⎢⎜⎟+⋅ ⎥

⎢⎝⎠ ⎥

⎣ ⎦





(8.16)

The quantity 'R is thereby the improvement of the reduction index due to the additional
lining. To calculate this improvement we shall need an expression for the radiation factor
VB. However, we have shown in Chapter 6 (section 6.4.2.1) that the radiated power from
a bending wave near field on a plate driven at a point and along a line, respectively, is
given by