Introduction to Acoustics

8
7
6
5
4
3
2
1
0
–1
–2
–3
Error due to phase mismatch (dB)
0
LKO– LK
–5 –10 –15
Fig. 25.13 Maximum error due to phase mismatch as
a function of the bias error index K for negative residual
intensity (upper curve) and for positive residual intensity
(lower curve) (After [25.38])
less than 1 dB (survey accuracy [25.25]), and a bias error
index of 10 dB corresponds to the error being less
than 0.5dB(engineering accuracy [25.25]). These values
correspond to the phase error of the equipment being
five and ten times less than the actual phase angle in the
sound field, respectively. The quantity δpIo − K is known
as the dynamic capability of the measurement system.
Many applications of sound intensity measurements
involve integrating the normal component of the intensity
over a surface. The global versions of (25.27) and
(25.28) are found by integrating the normal component
over a surface that encloses a source. The result is the
expressions
�
ˆPa = Î · dS
S
� Pa
= Pa
= Pa
⎛
⎜
⎝1 − ϕpe
� � � � ⎞
p2 rms ρc dS
S
�
⎟
⎠
k∆r I · dS
⎛
⎜
⎝1 + I0ρc
� � � � ⎞
p2 rms ρc dS
S
�
⎟
⎠
I · dS
p 2 0
⎛
⎜
⎝1 − I0ρc
� � � � ⎞
p2 rms ρc dS
S
⎟
� ⎠
Î · dS
p 2 0
S
S
S
−1
dB
, (25.30)
where Pa is the true sound power of the source within
the surface [25.35]. The condition expressed by (25.29)
Sound Intensity 25.3 Measurement of Sound Intensity 1063
still applies, although the pressure-intensity index now
involves averaging over the measurement surface.
Sources outside the measurement surface do not contribute
to the surface integral of the true intensity [the
denominator of the second term on the right-hand side
of (25.30)], but they invariantly increase the surface integral
of the mean square pressure (the numerator of the
second term), as demonstrated by the results shown in
Fig. 25.14. It follows that even a very small phase error
imposes restrictions on the amount of extraneous noise
that can be tolerated in sound power measurement with
a p–p sound intensity measurement system.
Other Sources of Error
It can be difficult to avoid that the intensity probe
is exposed to airflow, for example in measurements
near air-cooled machinery. Strictly speaking the p–p
measurement principle is simply not valid in such circumstances
[25.40]. However, practice shows that the
resulting fundamental error is insignificant in airflows
of moderate velocities (say, up to 10 m/s), and that
the false, low-frequency intensity signals produced by
turbulence are a more serious problem under such conditions.
Turbulence generates pressure fluctuations (flow
noise, unrelated to the sound field) that contaminate the
signals from the two microphones, and at low frequencies
these signals are correlated and thus interpreted by
the measurement system as intensity. The resulting false
intensity is unpredictable and can be positive or negative.
This is mainly a problem below 200 Hz [25.41].
A longer spacer helps reducing the problem, but the most
Field indicator (dB)
20
10
0
250 500 1k 2k 4k
One-third octave band center frequency (Hz)
Fig. 25.14 Pressure-intensity index on a surface enclosing
a noise source determined under three different conditions:
measurement using a reasonable surface (solid line);
measurement using an eccentric surface (dashed line); measurement
with strong background noise at low frequencies
(long dashes) (After [25.39])
Part H 25.3