Question

Parasaurolophus was a dinosaur whose distinguishing feature was a hollow crest on the head. The 1.3 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? (Use 350 m/s for the speed of sound.)
Enter your answers using two significant figures in ascending order separated by commas.
f = _______Hz, ________Hz, ________Hz

Answer 1

67.31 Hz, 201.92 Hz, 336.54 Hz

Step-by-step explanation:

Resonance also known as standing wave occur when a uniform tube is closed at one end and open at the other end.

For a resonance wave in a tube with length b, wavelength λ of resonance wave is 4b because a quarter wave is formed in the tube, that is,

λ = 4b.

When the speed of sound is c, the frequency of sound, f, is

f = c /λ,

and therefore,

f = c / ( 4b ).

From the question,

When c = 350 m/s and b = 1.3 m,

using the formula

fn = c / ( 4b ) × n (n = 1, 3, 5, ...).

The first three resonant frequencies are;

First resonance frequency is

f = 350 / (4*1.3) * 1 = 67.31 Hz

Second resonance frequency is

f = 350 / (4*1.3) * 3 = 201.92 Hz

Third resonance frequency is

f = 350 / (4*1.3) * 5 = 336.54 Hz