Building Acoustics

230 Building acoustics

Figure 6.16 Radiation index of a 4 mm thick aluminium panel, 2.7m x 3.4m, measured using different kinds of
excitation. Data from Venzke et al. (1973). Calculated data from Equation (6.48).

The radiation factor for forced vibrations by a sound field will necessarily be
dependent on panel dimensions and the actual wavelength, but also on the angle of sound
incidence. In building acoustics we shall primarily be interested in the radiation factor for
an incident diffuse field. Several alternative expressions exist in the literature, e.g. Sewell
(1970), Ljunggren (1991) and Novak (1995). We shall quote the first mentioned, which
may be written

f^2

11

ln( ) 0.16 F( ) , where ( 1)

(^24)
b
kS
kS a
σ
π

⎛⎞

=+−Λ+⎜⎟Λ=Λ>

⎝⎠ (6.49)

and where k is the wave number and F(Λ) = F(1/Λ) is denoted a shape function. Data for
this shape function may be taken from a table but a more practical solution will be to use
a polynomial approximation or similar.
Based on this equation, EN 12354–1 gives an approximate formula, where an upper
limit of 2 is applied to the value of σf, i.e. 10⋅lg(σf) has a maximum value of 3 dB.
Without making unduly large errors one may also leave out the shape function, because
F will vary between zero and 0.5 when b/a varies between one and 10, and also the last

63 125 250 500 1000 2000 4000 8000

Frequency (Hz)

-40

-30

-20

-10

0

10

10 lg

σ (

dB

)

Diffuse sound - measured

Mechanical - measured

Mechanical - calculated