Building Acoustics

Sound transmission 219

6.3.1.1 Examples using idealized sources

We shall start using the idealized type of sources, monopoles and dipoles, to illustrate the
concept of radiation factor. For a monopole we found in section 3.4.1 that the radiated
power could be expressed as

22

2

00 22 ,

1

a

ka

Wcu S

ka

=ρ

+

 (6.26)

where k is the wave number and a the radius of the sphere with area S = 4 π a^2. Inserting
this expression into Equation (6.25) giving the radiation factor, we get

22

monopole 22.

1

ka

ka

σ =

+

(6.27)

Examples on the radiation factor for a monopole source having radii of 5 and 25 cm,

respectively, are shown in Figure 6.8. The radiation factor is given on a logarithmic scale

as 10⋅lg σ, a quantity commonly denoted radiation index.

Figure 6.8 Radiation factor of a monopole (pulsating sphere) and a dipole (oscillating sphere) with radius 5 and
25 cm, respectively. Solid curves – monopole. Dashed curves – dipole.

The technical report ISO/TR 7849 (1987)^2 is using Equation (6.27) as an upper limit
when calculating the radiated noise from machinery based on measured vibration levels.
In this report it is expressed as

(^2) Currently (2007) under revision.
10 20 50 100 200 500 1000 2000 5000
Frequency (Hz)
-50
-40
-30
-20
-10
0
10 lg
σ (
dB)^25
5