Introduction to Acoustics

1118 Part H Engineering Acoustics
Part H 27.2
a) b) c) d)
Fig. 27.18a–d Measured vibration patterns of a guitar top plate (left) and the projected radiated sound fields from the
guitar (right): (a) and (b) at 600 Hz; (c) and (d) at 1200 Hz. Scanning vibrometry was used for both recordings. Observe
that in (b) and (d) it is the projected sound field across the guitar body that is measured [27.72]. (Reprint S. Hirzel Verlag,
Stuttgart)
Fig. 27.19 The sound field at 1303 Hz inside a saxophone cavity model measured with scanning vibrometry. The model is
a conical transparent model about 54 cm long with a rectangular cross section, excited at the mouthpiece end by a normal
saxophone mouthpiece and it has an artificial mouth
the acoustic waves emitted from the guitar by this vibration,
the guitar is rotated 90, so that the probing
laser light rays is passing in front of and in parallel
to the top plate. The probing laser then hits to a heavy,
rigid reflector and is reflected back again into the measuring
unit of the vibrometer instrument. The reflector
must be absolutely rigid, as in TV holography and
pulsed TV holography, to record sound fields, compare
Fig. 27.8.
The temporal and spatial pressure fluctuations
∆p(x, y, z, t), which are connected with acoustic or
fluidic phenomena, cause changes of the optical refractive
index ∆n(x, y, z, t) = n(x, y, z, t) − n0 and,
consequently, the rate of change of the measured optical
phase. In the simplest case a linear acoustic wave
travels in the x-direction in the measuring volume; compare
Fig. 27.8. Then the optical phase varies from point
to point but at each point it also varies sinusoidally with
time. This signal therefore behaves as a virtual displacement
of the rigid reflector. In real measurements the
acoustic wave is not ideally shaped in the measuring
volume (i.e. it is usually not two-dimensional) and a vibrometer
senses, by phase demodulation, a projected
virtual reflector displacement,
�
s(x, z, t) = ∆n(x, y, z, t)dy (27.10)
L
or by frequency demodulation, a virtual reflector velocity
�
ν(x, z, t) = ˙n(x, y, z, t)dy , (27.11)
L
i. e. the reflector seems to vibrate although it is immovable.
These virtual vibrations represent the acoustic
wave in the measuring volume. But, according to (27.10)
and (27.11), the integrated sum of all fluctuations of
the refractive index ∆n(x, y, z, t) along the laser beam
contributes to the measured result. An ideal measurement
situation is therefore a 2-D acoustic field as in
Fig. 27.8. If not, several projections may be used or, if
possible, enough that a tomographic reconstruction can
be obtained.
To study the sound generation in, and the sound
propagation from, a saxophone or a clarinet cavity, rectangular
model pipes (two-dimensional structures) with