141
Most of the theoretical and experimental work on directionalization has involved
several simplifications of the problem, some of which are more justifiable than
others:
1. The source is acoustically small, i.e. much smaller than a wavelength. This is
usually true. The sound speed in water is 1500 m/s, so the wavelength at 50 Hz
is 30 m and even at 1 kHz is 1.5 m. The source, often the swim bladder is of the
order of only a few centimeters in extent. One exception is ultrasonic hearing
exhibited by some clupeids (Mann et al. 1997, 1998) where the wavelength is of
the order of 1 cm and the presumed source, an echolocating dolphin, encompasses much of the head of the dolphin.
2. The source is monopole (omnidirectional) in character. Since all natural sources
within the hearing range of fish are acoustically small, significant sound can only
arise from monopole sources. Such sources generate sound by an oscillatory
change in volume which generally requires the presence of an air bubble. Wholebody acceleration of a fish produces dipole radiation, but it is very low in frequency and/or very small in amplitude (but see item 4 below for an important
exception).
3. The signal is sinusoidal. This mathematical and experimental convenience is
rarely appropriate. While some fish calls are near sinusoidal (e.g., midshipman
fish (Porichthys notatus) Bass et al. 1999; Bass and McKibben 2003) most fish
sounds consist of a sequence of broadband click-like sounds. Sinusoidal sounds
in the ocean are usually anthropogenic, natural oceanic noise is broadband.
4. The medium is unbounded. While for many pelagic fish the ocean boundaries
play no significant role in sound propagation, the bottom plays a significant role
for fish located close to the bottom or for very shallow water (Rogers and Cox
1988) The ocean surface, which presents a pressure-release boundary condition,
can effect sound propagation via the filtering Lloyd’s mirror effect or, if the
source is close enough to the surface by transforming a monopole source into a
vertically oriented dipole source (Urick 1967, p. 110).
Proposed mechanisms for resolving the 180° ambiguity have focused on phase
relationship between the acoustic pressure and particle velocity (Schuijf 1975;
Schellart and de Munck 1987; Rogers et al. 1988). It is known that for plane waves
or for spherical waves in the far field, pressure and acoustic particle velocity are in
phase for waves propagating in the +x or +r direction and 180° out of phase for
waves propagating in the opposite direction. In the near field of a monopole source
the ambiguity can be resolved by analysis of the phase between the pressure and
particle velocity and this has been proposed, by some (e.g., Schuijf 1975; Schellart
and de Munck 1987), as the mechanism used by fish. A principal difficulty with this
hypothesis is that it only applies only to sinusoidal sources away from the surface.
A more general approach to the problem of directionalization, which encompasses
the phase model, can be formulated based on the concept of time-averaged acoustic
intensity. Consideration of energy conservation in acoustics leads to the concept of
acoustic intensity (see Pierce 1981, Section 1-11 for a derivation of Eqs. 1–5):
Directional Hearing and Sound Source Localization in Fishes
Most of the theoretical and experimental work on directionalization has involved
several simplifications of the problem, some of which are more justifiable than
others:
1. The source is acoustically small, i.e. much smaller than a wavelength. This is
usually true. The sound speed in water is 1500 m/s, so the wavelength at 50 Hz
is 30 m and even at 1 kHz is 1.5 m. The source, often the swim bladder is of the
order of only a few centimeters in extent. One exception is ultrasonic hearing
exhibited by some clupeids (Mann et al. 1997, 1998) where the wavelength is of
the order of 1 cm and the presumed source, an echolocating dolphin, encompasses much of the head of the dolphin.
2. The source is monopole (omnidirectional) in character. Since all natural sources
within the hearing range of fish are acoustically small, significant sound can only
arise from monopole sources. Such sources generate sound by an oscillatory
change in volume which generally requires the presence of an air bubble. Wholebody acceleration of a fish produces dipole radiation, but it is very low in frequency and/or very small in amplitude (but see item 4 below for an important
exception).
3. The signal is sinusoidal. This mathematical and experimental convenience is
rarely appropriate. While some fish calls are near sinusoidal (e.g., midshipman
fish (Porichthys notatus) Bass et al. 1999; Bass and McKibben 2003) most fish
sounds consist of a sequence of broadband click-like sounds. Sinusoidal sounds
in the ocean are usually anthropogenic, natural oceanic noise is broadband.
4. The medium is unbounded. While for many pelagic fish the ocean boundaries
play no significant role in sound propagation, the bottom plays a significant role
for fish located close to the bottom or for very shallow water (Rogers and Cox
1988) The ocean surface, which presents a pressure-release boundary condition,
can effect sound propagation via the filtering Lloyd’s mirror effect or, if the
source is close enough to the surface by transforming a monopole source into a
vertically oriented dipole source (Urick 1967, p. 110).
Proposed mechanisms for resolving the 180° ambiguity have focused on phase
relationship between the acoustic pressure and particle velocity (Schuijf 1975;
Schellart and de Munck 1987; Rogers et al. 1988). It is known that for plane waves
or for spherical waves in the far field, pressure and acoustic particle velocity are in
phase for waves propagating in the +x or +r direction and 180° out of phase for
waves propagating in the opposite direction. In the near field of a monopole source
the ambiguity can be resolved by analysis of the phase between the pressure and
particle velocity and this has been proposed, by some (e.g., Schuijf 1975; Schellart
and de Munck 1987), as the mechanism used by fish. A principal difficulty with this
hypothesis is that it only applies only to sinusoidal sources away from the surface.
A more general approach to the problem of directionalization, which encompasses
the phase model, can be formulated based on the concept of time-averaged acoustic
intensity. Consideration of energy conservation in acoustics leads to the concept of
acoustic intensity (see Pierce 1981, Section 1-11 for a derivation of Eqs. 1–5):
Directional Hearing and Sound Source Localization in Fishes