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The crest of a Parasaurolophus dinosaur skull is shaped somewhat like a trombone and contains a nasal passage in the form of a long, bent tube open at both ends. The dinosaur may have used the passage to produce sound by setting up the fundamental mode in it. (a) If the nasal passage in a certain Parasaurolophus fossil is 2.0 m long, what frequency would have been produced? (b) If that dinosaur could be recreated (as in Jurassic Park), would a person with a hearing range of 60 Hz to 20 kHz be able to hear that fundamental mode and, if so would the sound be high of low frequency? Fossil skulls that contain shorter nasal passages are thought to be those of the female Parasaurolophus. (c) Would that make the female's fundamental frequency higher or lower than the male's?
SOLUTION
(a) We know that, and , we find
for the fundamental frequency in a nasal passage of length
(subject to various assumptions about the nature of the passage as a "bent tube open at both ends").
(b) The sound would be perceptible as sound (as opposed to just a general vibration) of very low frequency.
(c) Smaller implies larger by the formula cited above. Thus, the female's sound is of higher pitch (frequency).
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