Building Acoustics

Sound transmission 223

where we assume that kB < k. For increasing k, i.e. when the wavelength λB in the plate
increases in relation to the wavelength λ in air, the radiation factor approaches 1 (one).
This applies, as already demonstrated, for the idealized source types but also for plates of
finite dimensions.

6.3.3 Critical frequency (coincidence frequency)

In the above we introduced the notion of trace matching. The term was first introduced
in German literature (see e.g. Cremer et al. (1988)), describing the condition of the trace
wavelength in an incident wave equal to the wavelength of the plate, i.e. a reversed
situation of the one being described in the last section. In either case, there will be a
limiting or critical frequency where this coincidence phenomenon may occur, also called
the coincidence frequency. We shall use the former notion. At this frequency fc the
wavelength λB is equal to the wavelength λ in the surrounding medium. In other words:
the phase speed cB in the solid medium is equal to the phase speed c 0 in the surrounding
medium (air).

Figure 6.11 Critical frequency of homogeneous plates as a function of thickness.

For thin plates, i.e. when the wavelength is larger than approximately six times the
plate thickness, we have shown that the phase speed is expressed as

(^) B^4 ,

B

c

m

=⋅ω (6.40)

where B is the bending stiffness per unit length and m is the mass per unit area. By
putting cB equal to c 0 and solving with respect to frequency, we get

112 5 0120 50 00200

Plate thickness (mm)

100

1000

10000

200

500

2000

5000

C

ritical f

requency

fc

(Hz)

Concrete

Lightw. concrete

Steel, Al.

Glas

Chipboard

Plasterboard