Introduction to Acoustics

1058 Part H Engineering Acoustics
Part H 25.3
25.3 Measurement of Sound Intensity
Acousticians have attempted to measure sound intensity
since the early 1930s, but measurement of sound intensity
is more difficult than measurement of the sound
pressure, and it took almost 50 years before sound intensity
measurement systems came on the market. The first
international standards for measurements using sound
intensity and for instruments for such measurements
were issued in the middle of the 1990s. A description of
the history of the development of sound intensity measurement
up to the middle of the 1990s is given in Fahy’s
monograph Sound Intensity [25.2].
Measurement of sound intensity involves determination
of the sound pressure and the particle velocity
at the same position simultaneously. In the general
case at least two transducers are required. There are
three possible measurement principles: (i) one can determine
the particle velocity from a finite-difference
approximation of the pressure gradient using two closely
spaced pressure microphones and use the average of
the two microphone signals as the pressure [25.2, 13]
(the two-microphone or p–p method); (ii) one can combine
a pressure microphone with a particle velocity
transducer [25.2] (thep–u method); and (iii) one can
determine the pressure from a finite-difference approximation
of the divergence of the particle velocity [25.14]
(the u–u method). The first of these methods is well established.
The second method has been hampered by
the absence of reliable particle velocity transducers,
but with the recent advent of the Microflown particle
velocity sensor [25.15, 16] it seems to have potential
[25.17]. The third method, which involves three
matched pairs of particle velocity transducers, has never
been used in air and is mentioned here for the sake of
completeness.
25.3.1 The p–p Measurement Principle
For more than 25 years the p–p method based on two
closely spaced pressure microphones (or hydrophones)
has dominated sound intensity measurement. This
method relies on a finite-difference approximation to
the sound pressure gradient. Both the International Electrotechnical
Commission (IEC) standard on instruments
for the measurement of sound intensity and the corresponding
American National Standards Institute (ANSI)
standard deal exclusively with p–p measurement systems
[25.18, 19]. The success of this method is related
to the fact that condenser microphones are more stable
and reliable than any other acoustic transducer.
a) Pressure and particle velocity
0
0 62.5
b) Instantaneous intensity
Time (ms)
0
0 62.5
c) Intensity
Time (ms)
0
0 62.5
Time (ms)
Fig. 25.5 Measurement in a reverberation room driven with
one-third octave noise with a center frequency of 500 Hz.
Key as in Fig. 25.2 (After [25.7])
Two pressure microphones are placed close together.
The particle velocity component in the direction of the
axis through the two microphones r is obtained from
Euler’s equation of motion
∂p(t) ∂ur(t)
+ ρ = 0 , (25.19)
∂r
∂t
where the gradient of the pressure is approximated by
a finite difference. Thus the particle velocity is deter-
mined as
ûr(t) =− 1
ρ
�t
−∞
p2(τ) − p1(τ)
dτ , (25.20)
∆r
where p1 and p2 are the signals from the two microphones,
∆r is the microphone separation distance, and