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 = , ,

67.31 Hz, 201.92 Hz, 336.54 Hz

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

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