Introduction to Acoustics

258 Part B Physical and Nonlinear Acoustics
Part B 8.1
Also forces may be transmitted to the medium setting
it into motion, as exemplified by the phenomenon
of acoustic streaming. Acoustic radiation forces may
be used to levitate objects and keep them in traps. In
other areas of science this is accomplished by electrical
or electromagnetical forces (ion traps, optical tweezers).
Nonlinear acoustics is the subject of many books,
congress proceedings and survey articles [8.1–4, 6–19].
In liquids a special phenomenon occurs, the rupture
of the medium by sound waves, called acoustic cavitation
[8.20–27]. This gives rise to a plethora of special
effects bringing acoustics in contact with almost any
other of the natural sciences. Via the dynamics of the
cavities, or the cavitation bubbles produced, dirt can
be removed from surfaces (ultrasonic cleaning), light
8.1 Origin of Nonlinearity
All acoustic phenomena necessarily become nonlinear
at high intensities. This can be demonstrated when looking
at the propagation of a harmonic sound wave in air.
In Fig. 8.1 a harmonic sound wave is represented graphically.
In the upper diagram the sound pressure p is
plotted versus location x. The static pressure pstat serves
as a reference line around which the sound pressure oscillates.
This pressure pstat is normally about 1 bar. In the
lower diagram the density distribution is given schematically
in a grey scale from black to white for the pressure
range of the sound wave.
Assuming that the sound pressure amplitude is increased
steadily, a point is reached where the sound
pressure amplitude attains pstat giving a pressure of
pstat
p
Fig. 8.1 Graphical representation of a harmonic sound
wave
x
emission may occur upon bubble collapse (sonoluminescence
[8.28]) and chemical reactions are initiated
(sonochemistry [8.29, 30]).
Recently, the general theory of nonlinear dynamics
lead to the interesting finding that nonlinear dynamical
systems may not just show this simple scenario of
combination tones and self-actions, but complicated dynamics
resembling stochastic behavior. This is known
as deterministic chaos or, in the context of acoustics,
acoustic chaos [8.31, 32].
Nonlinear acoustics also appears in wave propagation
in solids. In this case, further, entirely different,
nonlinear phenomena appear, because not only longitudinal
but also transverse waves are supported. A separate
chapter of this Handbook is devoted to this topic.
zero in the sound pressure minimum. It is impossible
to go below this point as there cannot be less than
zero air molecules in the minimum. However, air can be
compressed above the pressure pstat just by increasing
the force. Therefore, beyond a sound pressure amplitude
p = pstat no harmonic wave can exist in a gas; it
must become nonlinear and contain harmonics. The obvious
reason for the nonlinearity in this case (a gas)
Resulting displacement
Soft
Hard
Applied force
Fig. 8.2 Symmetric nonlinear expansion and compression
laws compared to a linear law (straight dotted line) with
soft spring behavior (solid line) and hard spring behavior
(dashed line)