Introduction to Acoustics

162 Part A Propagation of Sound
Part A 5.2
Sound pressure spectrum level (dB re µPa)
146
126
106
86
66
Intermittent and local effects
Earthquakes
and explosions
Biologics
Precipitation
Ships, industrial activity
Sea ice
Key
Limits of prevailing noise
Wind-dependent bubble and spray noise
Low-frequency very-shallow-water
wind dependence
Heavy precipitation
Heavy traffic noise
Usual traffic noise - shallow water
Usual traffic noise - deep water
Thermal noise
General pattern of noise from
earthquakes and explosions
Extrapolations
Wind force
(Beaufort)
1
10
Frequency (Hz)
5
10 10 2
10 3
10 4
5
46
Prevailing noises
3
2
26
Turbulent-pressure
fluctuations
Oceanic traffic
1
6
Bubbles and spray
(surface agitation)
Surface waves – Second-order pressure effects
(Seismic background)
Molecular
agitation
Fig. 5.15 Composite of ambient noise spectra (after [5.24])
(1500 m/s) , a horizontal ray (θ = 0) launched from the
ocean surface would have an angle with respect to the
horizontal of about 11 ◦ at 300 m depth. All other rays
would arrive with greater vertical angles. Hence we expect
this horizontal notch. However, the horizontal notch
is often not seen at shipping noise frequencies. That is
because shipping tends to be concentrated in continentalshelf
regions and propagation down a continental slope
converts high-angle rays to lower angles at each bounce.
There are also deep-sound-channel shoaling effects that
result in the same trend in angle conversion.
The vertical directionality of noise in shallow water
has a simple environmental dependence [5.27]. For
example, in the summer with a downward refracting profile,
the same discussion as above leads to a horizontal
noise notch. However the vertical directionality of noise
from the surface in the winter tends to be driven by
8
bottom properties. Thus, if the bottom is not very lossy,
surface sources exciting low-order modes can come from
large distances (and hence large areas). These paths are
close to the horizontal and noise will then tend to have
a strong horizontal component. On the other hand, a very
lossy bottom will prevent long-range propagating paths
from contributing to the noise field and the noise will
tend to be local and subsequently vertical.
5.2.6 Bubbles and Bubbly Media
Bubbles not only occur naturally in the ocean, but the
swim bladders of fish can also be thought of as bubbles.
The physics of bubbles is a large area of activity
in acoustics [5.7, 28]. Here we will confine ourselves to
some aspects relevant to ocean acoustics. First we discuss
some properties of bubbles in terms of resonators,
scatterers and then go on to some aspects of bubbly
media and scattering from bubbles.
Bubble scattering follows two regimes depending
on the magnitude of the bubble radius oscillations in
response to the incident fluctuating pressure field [5.29]:
1. For small pressure amplitudes, the response is linear.
The first step in any linear analysis is the identification
of the resonance frequency of an oscillating
bubble and the measurement of the bubble scattering
cross section.
2. Due to nonlinear terms in the governing equations,
the response of a bubble will be affected by nonlinearities
as the amplitude of the pressure field is
increased. In this case, the bubble may continue to
oscillate stably (stable acoustic cavitation) generating
(sub)harmonics in the scattered field. Under
other circumstances, the change in bubble size during
a single cycle of oscillation becomes so large
that the bubble undergoes a cycle of explosive cavitation
growth and violent collapse. Such a response
is termed transient acoustic cavitation and is distinguished
from stable acoustic cavitation by the fact
that the bubble radius changes by several orders of
magnitude during each cycle.
The Bubble as a Scatterer
The calculation of the natural acoustic resonance of an
oscillating bubble in the linear regime requires considerable
algebra combining: (1) the equation of motion,
(2) mass conservation, and (3) continuity relations at
the bubble surface. These developments go beyond the
scope of this chapter. In the following, we simply summarize
the final results, which are the expression of the