Question

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? Assume a speed of sound of 350 m/s.

Answer 1

Answer:

58.33 Hz

175 Hz

291.67 Hz

Explanation:

L = Length of tube = 1.5 m

v = Speed of sound in air = 350 m/s

The first resonant frequency is given by

$f_1=\dfrac{v}{4L}\\\Rightarrow f_1=\dfrac{350}{4\times 1.5}\\\Rightarrow f_1=58.33\ Hz$

The first resonant frequency is 58.33 Hz

The second resonant frequency is given by

$f_2=3\dfrac{v}{4L}\\\Rightarrow f_2=3\dfrac{350}{4\times 1.5}\\\Rightarrow f_2=175\ Hz$

The first resonant frequency is 175 Hz

The third resonant frequency is given by

$f_3=5\dfrac{v}{4L}\\\Rightarrow f_3=5\dfrac{350}{4\times 1.5}\\\Rightarrow f_3=291.67\ Hz$

The first resonant frequency is 291.67 Hz