Introduction to Acoustics

a) Pressure and particle velocity
0
0 125
Time (ms)
b) Instantaneous intensity
0
0 125
Time (ms)
c) Intensity
0
0 125
Time (ms)
Fig. 25.3 Measurement in the near field of a loudspeaker
driven with one-third octave noise with a center frequency
of 250 Hz. Key as in Fig. 25.2 (After [25.7])
where ˜p(t) andũ(t) are the Hilbert transforms of the
pressure and the particle velocity [25.12]. The time average
of this quantity in a steady sound field is the complex
intensity given by (25.15).
In a narrow-band sound field the real and imaginary
parts of the complex instantaneous intensity are lowpass
signals that represent short-time average values of
the two components of (25.15) [25.7].
Figure 25.2 shows the result of a measurement at
a position 30 cm (about one wavelength) from a small
loudspeaker driven with a band of one-third octave noise.
The sound pressure and the particle velocity (multiplied
by ρc) are almost identical; therefore the instantaneous
intensity is always positive, and the real part of the
complex instantaneous intensity is much larger than
Sound Intensity 25.2 Active and Reactive Sound Fields 1057
a) Pressure and particle velocity
0
0 125
Time (ms)
b) Instantaneous intensity
0
0 125
Time (ms)
c) Intensity
0
0 125
Time (ms)
Fig. 25.4 Measurement 30 cm from a vibrating steel box
driven with one-third octave noise with a center frequency
of 250 Hz. Key as in Fig. 25.2 (After [25.7])
the imaginary part. This is an active sound field. Figure
25.3 shows the result of a similar measurement at
a distance of a few centimeters (less than one tenth of
a wavelength) from the loudspeaker cone. In this case
the sound pressure and the particle velocity are almost
in quadrature, and as a result the instantaneous intensity
fluctuates about zero, that is, sound energy flows
back and forth, out of and into the loudspeaker, and the
imaginary part of the complex instantaneous intensity
is much larger than the real part. This is an example of
a strongly reactive sound field. Figure 25.4 shows data
measured about 30 cm from a vibrating box made of
3 mm steel plates. It is apparent that the vibrating structure
generates a much more complicated sound field
than a loudspeaker does. And finally Fig. 25.5 shows the
result of a measurement in a reverberant room several
meters from the loudspeaker generating the sound field.
Here the sound pressure and the particle velocity appear
to be uncorrelated signals; this is neither an active nor
a reactive sound field; this is a diffuse sound field.
Part H 25.2