46
D.R. Ketten
for this discussion, we will assume that cetaceans deal with in-water sound
speed and wave lengths that are simply 4.5 times greater than in air.
Mammalian ears are generally considered to be intensity detectors (Yost
1994), although the theory that some marine mammals are simple pressure
detectors has been proposed. Pressure and intensity are related but are not
synonymous. In-air measures of hearing make little distinction between the
two, but modeling an ear in water as a pressure versus intensity transducer
has far-reaching consequences.
Sound intensity (I) is the acoustic power impinging on a surface perpendicular to the direction of sound propagation; i.e., the sound energy per
second per unit area. Intensity is power/unit area (I = Pia). Therefore, intensity can be rewritten as the product of sound pressure (p) and vibration
velocity (v): I = pv. For a traveling spherical wave, the velocity component
becomes particle velocity (u), which is defined in terms of effective sound
pressure (p) and the characteristic impedance of the medium, which is the
product of the speed of sound (c) and density of the medium (p): u(x,t) =
p/pc.
For an instantaneous sound pressure in an outward traveling plane
wave, intensity in terms of pressure, density, and sound speed is: I =
pv = p(p/pc) = p2/pC. If we assume average sound speeds and densities
for surface air (c = 340rn/s; r = O.OO13g1cc) and sea water (c = 1,530rn/s;
P = 1.03 glCC):
lair = p2 /(340 m/s)(O.0013 g/cc) = p2 /(0.442g - m/s- cc)
Iwater =p2 /(1,530 m/s)(1.03 g/cc) =p2 /(1,575 g- m/s- cc)
To understand the sensory implications of these equations, consider a hypothetical, perfectly amphibious mammal. To hear equally well in water and
in air with an intensity-based ear would require the same acoustic
power/unit area in water as in air; that is, (lair = Iwaler):
lair =p2air /(0.442 g - mls - cc) =p2waler /(1,575 g - mls - cc) =Iwaler
or
p2 ai ,(3,565.4) =p2waler
and
Pai,(59.7) =Pwaler
which means this theoretical transmedia ear would require a received sound
pressure nearly 60-fold greater in water than in air for an equivalent
acoustic percept.
Although the most appropriate measure of intensity is watts/m 2 , we capitalize on the fact that intensity is related to the mean square pressure of
the sound wave over time and use effective sound pressure level (SPL),
which is easier to determine, to describe hearing thresholds. Sound pressure
levels are conventionally expressed in decibels (dB), defined as: dB SPL =
1010g(p2 m /p2 r ) = 2010g(Pm/Pr) where pm is the pressure measured and Pr is
an arbitrary reference pressure. Given identical reference pressures, our
idealized amphiboid needs a sound level -35.5 dB greater in water than in
air (10 log 3,565.4), but conventionally, two reference pressures are used. For
D.R. Ketten
for this discussion, we will assume that cetaceans deal with in-water sound
speed and wave lengths that are simply 4.5 times greater than in air.
Mammalian ears are generally considered to be intensity detectors (Yost
1994), although the theory that some marine mammals are simple pressure
detectors has been proposed. Pressure and intensity are related but are not
synonymous. In-air measures of hearing make little distinction between the
two, but modeling an ear in water as a pressure versus intensity transducer
has far-reaching consequences.
Sound intensity (I) is the acoustic power impinging on a surface perpendicular to the direction of sound propagation; i.e., the sound energy per
second per unit area. Intensity is power/unit area (I = Pia). Therefore, intensity can be rewritten as the product of sound pressure (p) and vibration
velocity (v): I = pv. For a traveling spherical wave, the velocity component
becomes particle velocity (u), which is defined in terms of effective sound
pressure (p) and the characteristic impedance of the medium, which is the
product of the speed of sound (c) and density of the medium (p): u(x,t) =
p/pc.
For an instantaneous sound pressure in an outward traveling plane
wave, intensity in terms of pressure, density, and sound speed is: I =
pv = p(p/pc) = p2/pC. If we assume average sound speeds and densities
for surface air (c = 340rn/s; r = O.OO13g1cc) and sea water (c = 1,530rn/s;
P = 1.03 glCC):
lair = p2 /(340 m/s)(O.0013 g/cc) = p2 /(0.442g - m/s- cc)
Iwater =p2 /(1,530 m/s)(1.03 g/cc) =p2 /(1,575 g- m/s- cc)
To understand the sensory implications of these equations, consider a hypothetical, perfectly amphibious mammal. To hear equally well in water and
in air with an intensity-based ear would require the same acoustic
power/unit area in water as in air; that is, (lair = Iwaler):
lair =p2air /(0.442 g - mls - cc) =p2waler /(1,575 g - mls - cc) =Iwaler
or
p2 ai ,(3,565.4) =p2waler
and
Pai,(59.7) =Pwaler
which means this theoretical transmedia ear would require a received sound
pressure nearly 60-fold greater in water than in air for an equivalent
acoustic percept.
Although the most appropriate measure of intensity is watts/m 2 , we capitalize on the fact that intensity is related to the mean square pressure of
the sound wave over time and use effective sound pressure level (SPL),
which is easier to determine, to describe hearing thresholds. Sound pressure
levels are conventionally expressed in decibels (dB), defined as: dB SPL =
1010g(p2 m /p2 r ) = 2010g(Pm/Pr) where pm is the pressure measured and Pr is
an arbitrary reference pressure. Given identical reference pressures, our
idealized amphiboid needs a sound level -35.5 dB greater in water than in
air (10 log 3,565.4), but conventionally, two reference pressures are used. For