Building Acoustics

Sound transmission 245

2

2

w

w 0

0

11 cos

, 10lg 10lg 1.

cos 2

1

2

Z

R

Z Z

Z

φ

τ

φ τ

⎡ ⎤

==⋅=⋅⎢ +⎥

+ ⎢ ⎥

⎣ ⎦

(6.98)

The wall impedance Zw will here be given by Equation (6.91). An example using these
equations is shown in Figure 6.22, where the sound reduction index of a plate of surface
weight 10 kg/m^2 and critical frequency 1000 Hz is given for a number of incident angles.
The low values around the critical frequency should be noted, furthermore, how
this “dip” approaches the critical frequency by increasing the angle should also be
observed. The determining factor in this frequency range is the damping of the plate
characterized by the loss factor, which in this example is rather high. We shall further
note that the mass law gives an appropriate description at frequencies somewhat lower
than the critical frequency. Above coincidence we observe that the dependence on
frequency is much greater than the corresponding one in the mass law range. The
bending stiffness will be the determining factor, and far above coincidence there will be
an increase of 18 dB per octave.

Figure 6.22 Sound reduction index of an infinitely large plate with the angle of incidence as parameter.
Material data: m − 10 kg/m^2 , η − 0.1, fc − 1000 Hz.

6.5.1.4 Sound reduction index by diffuse sound incidence

On real partitions in buildings we normally have sound incidence from many angles at
the same time. To calculate the sound insulation we could in principle use Equations
(6.98) and (6.91), make a weighting according to the given distribution of incident angles
and sum up the contributions. In practice, however, the actual distribution is seldom
known. As mentioned in the introduction, the only viable solution is then to carry out the

100 200 500 1000 2000 5000 10000

Frequency (Hz)

0

10

20

30

40

50

60

Sound

reduction index (dB)

φ = 80

φ = 60

φ = 40

φ = 20

φ = 0

fc