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J.L. Aroyan et al.
oscillating valves in an anatomical cross section. The V-fold has been the
preferred oscillatory valve for some researchers (Haldiman and Tarpley
1993; Reidenberg and Laitman 1993), while the arytenoid cartilages have
been the preferred oscillatory valve mechanism for others (Sukhovskaya
and Yablokov 1979; Purves and Pilleri 1983). The presence of welldeveloped laryngeal folds in the blue whale is described by Beauregard and
Boulart (1882), as well as the ability of the paired arytenoid cartilage to
close the opening between trachea and laryngeal sac. It may be possible to
better determine the roles of the arytenoids and the vocal folds if we can
further validate a sound production model. One relevant aspect to consider
might be whether the oscillator is reversible. Can the oscillator produce a
similar sound from an airflow in either direction? We assume the whale
provides muscle control over the oscillating valve, determining the call
character.
7.3 Resonators
The calculation of accurate pipe, Helmholtz, or bubble resonance frequencies in the blue whale is beyond the scope of our anatomical knowledge
and generally beyond the scope of this discussion even if we were to make
the needed biological assumptions. This topic continues to be the subject of
considerable importance and interest however, thus we offer some observations. Given the range in the fundamental frequency of the blue whale,
both geographic and within a single call, a resonator would have to be of
relatively low 0 (resonance quality factor) to be sufficiently broad to aid
the animal in sound production. Resonance quality factor (0) is proportional to the energy expended per cycle to the energy stored in the system.
High 0 systems reduce the amount of air required because the volume of
the resonant cavity varies each cycle by more than the volume admitted
through the valve. While it has been suggested that low 0 bubble resonators
would still be useful (Barham 1973), we find a bubble resonator much less
applicable than a Helmholtz resonator because it appears difficult to maintain a significant bubble resonance over the depth range required by our
model. There are many formulas for bubble resonance, all of which may be
correct under different assumptions used to simplify the complexity of the
problem in the biological system, but these formulas do not suggest that a
significant resonance could be maintained over a significant portion of the
depth range from surface to collapse at 90m, thus limiting the calling whale
to a relatively narrow depth range. A Helmholtz resonator consists of an
enclosed volume vented through a pipe. On an anatomical basis we suggest
the laryngeal sac and nasal passage volume seems a more likely resonator
than the total air volume (Barham 1973) given the separation of the two
systems at the arytenoids and the relative stability of resonance frequencies within the laryngeal-nasal volume. If the laryngeal sac and nasal
passages act as a resonator, then a fluctuating stream of air through the
J.L. Aroyan et al.
oscillating valves in an anatomical cross section. The V-fold has been the
preferred oscillatory valve for some researchers (Haldiman and Tarpley
1993; Reidenberg and Laitman 1993), while the arytenoid cartilages have
been the preferred oscillatory valve mechanism for others (Sukhovskaya
and Yablokov 1979; Purves and Pilleri 1983). The presence of welldeveloped laryngeal folds in the blue whale is described by Beauregard and
Boulart (1882), as well as the ability of the paired arytenoid cartilage to
close the opening between trachea and laryngeal sac. It may be possible to
better determine the roles of the arytenoids and the vocal folds if we can
further validate a sound production model. One relevant aspect to consider
might be whether the oscillator is reversible. Can the oscillator produce a
similar sound from an airflow in either direction? We assume the whale
provides muscle control over the oscillating valve, determining the call
character.
7.3 Resonators
The calculation of accurate pipe, Helmholtz, or bubble resonance frequencies in the blue whale is beyond the scope of our anatomical knowledge
and generally beyond the scope of this discussion even if we were to make
the needed biological assumptions. This topic continues to be the subject of
considerable importance and interest however, thus we offer some observations. Given the range in the fundamental frequency of the blue whale,
both geographic and within a single call, a resonator would have to be of
relatively low 0 (resonance quality factor) to be sufficiently broad to aid
the animal in sound production. Resonance quality factor (0) is proportional to the energy expended per cycle to the energy stored in the system.
High 0 systems reduce the amount of air required because the volume of
the resonant cavity varies each cycle by more than the volume admitted
through the valve. While it has been suggested that low 0 bubble resonators
would still be useful (Barham 1973), we find a bubble resonator much less
applicable than a Helmholtz resonator because it appears difficult to maintain a significant bubble resonance over the depth range required by our
model. There are many formulas for bubble resonance, all of which may be
correct under different assumptions used to simplify the complexity of the
problem in the biological system, but these formulas do not suggest that a
significant resonance could be maintained over a significant portion of the
depth range from surface to collapse at 90m, thus limiting the calling whale
to a relatively narrow depth range. A Helmholtz resonator consists of an
enclosed volume vented through a pipe. On an anatomical basis we suggest
the laryngeal sac and nasal passage volume seems a more likely resonator
than the total air volume (Barham 1973) given the separation of the two
systems at the arytenoids and the relative stability of resonance frequencies within the laryngeal-nasal volume. If the laryngeal sac and nasal
passages act as a resonator, then a fluctuating stream of air through the