Building Acoustics

62 Building acoustics

Figure 3.2 a) Intensity: power through a surface of area 1 m^2 normal to the direction of wave propagation. b)
The intensity integrated over a closed surface gives the total emitted power of a source.

With the term sound intensity is meant the sound power transmitted through a surface
area of 1 m^2 perpendicular to the direction of propagation (Figure 3.2). When using the
terms sound intensity and sound power it is normally understood that these are time-
averaged quantities. However, for completeness we shall also introduce the instantaneous
quantities as well. The intensity is, analogous to the particle velocity, a vector quantity
and is given by the product of the sound pressure at a point and the associated particle
velocity, i.e. expressed as

Iv()tpt t=⋅() () (watt/m )^2. (3.28)

The time-averaged sound intensity is ideally defined by the expression

0

1

lim ( ) ( ) d ,

T

T T pt t t

⇒∞T

Iv=⋅⋅∫ (3.29)

where T is the measuring time, which in practice must certainly be finite. The total sound
power emitted from a given source is found by integrating the time-averaged intensity
over a surface completely enclosing the source

WSIS=⋅= ⋅vv∫∫InTTdd(watt),n (3.30)

where n denotes the unit vector normal to an element dS of the surface. The quantity ITn
is then the component of the intensity in the normal direction, the normal time-averaged
sound intensity often being abbreviated to normal sound intensity. It should be noted that
this quantity is a signed one. In the same way as for the sound pressure level we define a
normal (time-averaged) sound intensity level as

(^) n n
0
IT 10 lg T (dB).

I

L

I

⎡⎤

=⋅⎢⎥

⎣⎦

(3.31)

1 m^2

a) b)