Building Acoustics

236 Building acoustics

It could be useful to give an example illustrative of the sound power due to this
bending near field. We shall then make a comparison with the radiated sound power
from a given area of an infinite plate, in conformity with defining the radiation factor.
We envisage this area as a piston having radius a. Setting the velocity amplitude equal to
u 0 the radiated sound power will be given by

Wcaupiston=ρπ0 0^22  0. (6.63)

The task is now to find the radiated sound power due to the near field according to
Equation (6.62) having velocity u 0 in the driving point. Second, we shall calculate the
radius a of the piston when Wpoint is equal to Wpiston. From Equations (6.50) and (6.51)
together with Equation (6.41), we obtain

32

00 0

point 32

c

8

cu

W

f

ρ

π

=⋅



(6.64)

Equating this sound power with Wpiston we obtain

2 00

cc

22

0.29.

cc

a

π f f

=⋅≈ (6.65)

Example The critical frequency fc of a concrete plate, having a thickness of 50 mm, will
be approximately 380 Hz (see Figure 6.11). The radius a of the equivalent piston source
will thereby be ≈ 26 cm. Using e.g. an applied force of 10 N (RMS-value) we get from
Equation (6.62) a radiated sound power of approximately 4.2⋅ 10 -6 watts or a sound power
level LW re 10-12 watts of 66 dB. Assuming a semicircular radiation centred on the driving
point the sound pressure level Lp will be 58 dB at a distance of 1 metre.
In several practical cases, it is important to know the radiated power from the
bending near field, not only when a point force drives the plate, but also equally well
when driven along a line. The latter applies to cases where vibrations are transmitted to a
panel or wall by studs or stiffeners. Corresponding expressions to the ones given in
Equations (6.62) and (6.64) are

222

0000

line 2 c

c

2

when.

Fcu

Wff

m f

ρρ

ω π

=⋅= ⋅A <<

 

AA (6.66)

The quantities Fℓ and ℓ are the force per unit length and the length of the line,
respectively.

6.4.2.2 Total sound power emitted from a plate

We have already presented an expression giving the total acoustical power emitted from
one side of a point-excited plate (see Equation (6.61)). By inserting the expression for the
power radiated from the near field, Equation (6.62) and using Equation (6.55), giving the
mean square velocity, we obtain