Popular version of paper 4pABa2
Presented Thursday Afternoon, December 4, 1997
134th ASA Meeting, San Diego, CA
Embargoed until December 4, 1997
Most male frogs and toads that make vocal sounds have an elastic pouch, called the vocal sac, which is connected to their oral cavity. Presumably, this structure is associated with the vocalization process in frogs. However, no one had ever worked out the details of such an association. Some species vocalize without a vocal sac, suggesting that the vocal sac is not required for producing sound. Instead, it has been proposed, the vocal sac may somehow amplify the sound signal or otherwise enhance the vocalization process. Sound enhancement could be related to an increase in the efficiency in which the sound is radiated, a change in the acoustical spectrum of the call by filtering out certain frequencies, or both. Additionally, benefits could arise if the presence of the vocal sacs leads to an increase in the oral cavity's "effective compliance." Compliance here can be understood as a measurement of how easy it is to pump air into the oral cavity--the higher the compliance, the easier it is. An increased effective compliance could significantly conserve energy during vocalization and enhance control over vocal-cord vibration. These last two hypotheses (i.e., enhanced control and increased compliance) could by themselves be sufficient to explain why vocal sacs evolved in these creatures while preventing the need to ascribe any direct sound-producing function to these structures. In this paper I explore these different hypotheses and present evidence supporting the function of the vocal sac as a structure amplifying the sound that originates in the vocal cords.
Historical perspective
Up to this point the mechanism responsible for transmitting sound energy from the frog larynx to the external air has remained elusive. Previous studies addressed the problem from different standpoints, and the vocal sac, the most obvious component of the sound-radiating system, was the target of most of these studies. It has been proposed that the vocal sac acts as a "resonator" for sound waves, amplifying the sound first produced in the frog's vocal cords.
In general, a resonator is a structure that can produce a special type of wave known as a standing wave under the right conditions. Sound waves are simply repeating patterns of compression and expansion in air. Associated with these patterns are points of maximum expansion and points of maximum compression. In ordinary "traveling" waves these points move, but in standing waves they stay fixed in space. As a result, standing waves can build up to very high intensities if energy is added to it in the proper fashion. To sustain a standing wave, a force must be applied periodically to the resonator at a rate equal to the object's natural "resonance" frequency. The resonance frequency depends on the structure's particular properties such as its size, shape, and stiffness. A resonator would improve the ability of the frog to transmit sound in much the same way as the wooden body of a guitar amplifies the sound created by its vibrating strings.
The appeal of this idea resides in the fact that when a force is applied to a resonator at the natural resonance frequency, one can maximize the amount of sound energy broadcast to the outside world. The unusually loud vocal sounds of frogs suggest that its vocalization system is operating at or close to resonance. Consequently it seemed logical that the vocal sac should act as a resonator, and many workers attempted to demonstrate this point. All attempts to demonstrate the existence of resonance failed however, seemingly indicating that resonance in the vocal sac was not taking place. Was this experimental evidence irrefutable proof of lack of resonance? Perhaps there were alternative interpretations for these observations, and the resonant character of the vocal sac was simply elusive but not non-existent. Indeed, previous work assumed that the resonating structure of the vocal sac was a structure with rigid walls. However, these assumptions ultimately break down because of the vocal sac is not a rigid structure but a compliant one. Therefore, these tests did not rule out resonance in general, instead they show that the structures being tested do not behave as rigid-walled resonators. Could they be something else?
A new approach
An alternative to resonance taking place in the air inside the vocal sac is resonance taking place on the walls of the vocal sac. This approach is fundamentally different from all that have come before, because it frames the problem using a completely different class of models, models based on the theory of vibrations of elastic membranes. These models are appropriate for describing the vibrational behavior of diverse structures ranging from bubbles to drumheads. In this new class of models, the standing waves required for resonance are formed not in the air associated with the vocal tract but instead on the elastic membranes associated with it (e.g., the vocal sac). Because the vibration patterns on these membranes can be described by equations that actually take into account the flexible nature of these structures, they allow a closer match between the theoretical approximation and the physical reality of frogs. Membrane resonator models generate resonances that are orders of magnitude lower in frequency than those generated by similar-sized rigid-walled resonator models. This is because the propagation velocity of the waves in the membrane is much lower than that in air (for example, 5 m/s in the throat area of bullfrogs versus 340 m/s in air). When the wave passes from a high-speed medium (air) to a low-speed medium (the vocal sac), there is a decrease in its "wavelength," the distance between successive points of maximum disturbance in the wave. This decreased wavelength allows relatively small structures such as the vocal sac to fit at least half a wavelength. Before reaching the membrane, these waves have wavelengths many times larger than the structure itself. Because of this phenomenon (and recalling that the condition for resonance is for the structure to be able to accommodate at least 1/2 wavelength or integer multiples of this quantity (1/2,1,11/2 etc) inside itself), structures of modest size are able to resonate at low frequencies that are unthinkable for rigid-walled resonators.
Testing the Hypothesis
To test these ideas I measured the tuning properties of the vocal sac
and other structures in several species of frogs (North American bullfrog,
leopard frog, Pacific treefrog, Western chorus frog, and barking
treefrog). In all the species tested, I found that the vocal sac (and certain
other soft structures) resonate at one or more of the frequencies emphasized
in the frog's natural call. There is also substantial evidence that some
of the frequencies present in the calls are radiated through the body wall
via the lungs. These specialized areas at the side of the body consistently
appeared to be tuned to the lowest frequency present in the calls. Not
only do these resonant structures radiate the calls, but they also shape
the tonal quality of the calls. These processes are analogous to those
occurring in humans when the voice is modified by changing the configuration
of the vocal tract. North American bullfrogs have a particularly unusual
sound-radiating system. In addition to the resonating vocal sac and throat,
bullfrogs have enlarged eardrums that resonate at
most of the frequencies present in the call. In this species the eardrums
are responsible for radiating 98% of the energy present in the call. The
vibrations of the eardrums are so large that you can actually see the eardrums
move when a bullfrog is calling. My work provides compelling
evidence that resonance does take place in frog vocal sacs and in certain
other soft structures of frog bodies. Moreover, these resonant structures
are the primary mechanism used to couple the energy from the vocal cords
to the environment and in so doing sculpt the spectrum of the call.
Further reading
Fletcher, N. H. (1992). Acoustic systems in biology. New York, Oxford University Press.
Fletcher, N. H. and S. Thwaites (1979). "Physical models for the analysis of acoustical systems in biology." Quarterly Review of Biophysics 12(1): 25-65.
Purgue, A. P. (1997). "Tympanic sound radiation in the bullfrog Rana catesbeiana." Journal of Comparative Physiology A. 181: 438-445