to seem smaller than it is. In general, however, we expect this manipulation
to be in the direction of size exaggeration; regardless of whether the
receiver in question is a competitor or a potential mate, it will typically
benefit the sender to seem larger than it is. Thus, we will focus on constraints
that might prevent the production of low frequencies or morphological
innovations that might allow it.
2.3.3. Body Size and Acoustic Impedance Constraints
The most fundamental limitation on the generation and propagation of
low-frequency sounds comes from impedance-matching requirements.
Although a small body may produce low-frequency oscillations, its ability
to convert energy from these oscillations to acoustic energy in the environment is limited by the relationship of oscillator size to the wavelength of
the generated sound. In general, wavelengths longer than twice the length
of the vibrator will be very ineffectively transmitted to the environment,
and lower frequencies will suffer even worse attenuation (Beranek 1954).
A good example is provided by a tuning fork, which is nearly inaudible
when vibrating freely in air but is quite loud when placed on a large surface
(a tabletop or the sounding board of a musical instrument). Mechanical
vibrations set up on a large surface couple to the air much more effectively
than those isolated to the moving tines of the fork itself. The difficulty in
radiating low-frequency sounds, called an impedance mismatch, provides a
physical constraint on the production of low-frequency sounds by small
animals.
The most frequent evolutionary solution to this problem appears to be
the use of various types of air sacs, which are interposed between the vibrating structures (e.g., the vocal folds or the air in the vocal tract) and the
environment. A detailed description was given earlier, in Section 2.2. Air
sacs are ubiquitous in anurans, and a role as impedance-matching systems
appears to be undisputed (see, e.g., Ryan 1985; Bradbury and Vehrencamp
1998). By increasing the size of the vibrating structure, anuran air sacs allow
their bearers to more effectively radiate lower frequencies to the environment than would otherwise be possible given their small body size.
However, some anurans lack sacs, which may be related to underwater
vocalization where there is no impedance mismatch (Hayes and Krempels
1986). A similar example is provided by some nonhuman primates in which
puncturing and subsequent deflation of laryngeal air sacs results in an attenuation of the radiated low-frequency sound but no change in pitch (Gautier
1971).
An impedance-matching function was also proposed for those cases of
avian tracheal elongation in which the trachea invaginates the sternum (e.g.,
cranes, trumpeter swans) by Gaunt and colleagues (Gaunt and Wells 1973;
Gaunt et al. 1987). Gaunt and his colleagues reasoned that the entire
sternum of such birds could be like the sounding board of a stringed
3. Unpacking “Honesty”
99
to be in the direction of size exaggeration; regardless of whether the
receiver in question is a competitor or a potential mate, it will typically
benefit the sender to seem larger than it is. Thus, we will focus on constraints
that might prevent the production of low frequencies or morphological
innovations that might allow it.
2.3.3. Body Size and Acoustic Impedance Constraints
The most fundamental limitation on the generation and propagation of
low-frequency sounds comes from impedance-matching requirements.
Although a small body may produce low-frequency oscillations, its ability
to convert energy from these oscillations to acoustic energy in the environment is limited by the relationship of oscillator size to the wavelength of
the generated sound. In general, wavelengths longer than twice the length
of the vibrator will be very ineffectively transmitted to the environment,
and lower frequencies will suffer even worse attenuation (Beranek 1954).
A good example is provided by a tuning fork, which is nearly inaudible
when vibrating freely in air but is quite loud when placed on a large surface
(a tabletop or the sounding board of a musical instrument). Mechanical
vibrations set up on a large surface couple to the air much more effectively
than those isolated to the moving tines of the fork itself. The difficulty in
radiating low-frequency sounds, called an impedance mismatch, provides a
physical constraint on the production of low-frequency sounds by small
animals.
The most frequent evolutionary solution to this problem appears to be
the use of various types of air sacs, which are interposed between the vibrating structures (e.g., the vocal folds or the air in the vocal tract) and the
environment. A detailed description was given earlier, in Section 2.2. Air
sacs are ubiquitous in anurans, and a role as impedance-matching systems
appears to be undisputed (see, e.g., Ryan 1985; Bradbury and Vehrencamp
1998). By increasing the size of the vibrating structure, anuran air sacs allow
their bearers to more effectively radiate lower frequencies to the environment than would otherwise be possible given their small body size.
However, some anurans lack sacs, which may be related to underwater
vocalization where there is no impedance mismatch (Hayes and Krempels
1986). A similar example is provided by some nonhuman primates in which
puncturing and subsequent deflation of laryngeal air sacs results in an attenuation of the radiated low-frequency sound but no change in pitch (Gautier
1971).
An impedance-matching function was also proposed for those cases of
avian tracheal elongation in which the trachea invaginates the sternum (e.g.,
cranes, trumpeter swans) by Gaunt and colleagues (Gaunt and Wells 1973;
Gaunt et al. 1987). Gaunt and his colleagues reasoned that the entire
sternum of such birds could be like the sounding board of a stringed
3. Unpacking “Honesty”
99