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13 January, 08:34

Parasaurolophus was a dinosaur whose distinguishing feature was a hollow crest on the head. The 1.5-m-long hollow tube in the crest had connections to the nose and throat, leading some investigators to hypothesize that the tube was a resonant chamber for vocalization. If you model the tube as an open-closed system, what are the first three resonant frequencies?

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  1. 13 January, 08:54
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    f1 = 58.3Hz, f2 = 175Hz, f3 = 291.6Hz

    Explanation:

    lets assume speed of sound is 350 m/s.

    frequencies of a standing wave modes of an open-close tube of length L

    fm = m (v/4L)

    where m is 1,3,5,7 ...

    and fm = mf1

    where f1 = fundamental frequency

    so therefore: f1 = 350 x 4 / 1.5

    f1 = 58.3Hz

    f2 = 3 x 58.3

    f2 = 175Hz

    f3 = 5 x 58.3

    f3 = 291.6Hz
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