A tube of length 1m is open on one end and closed on the other end. A sound sour

Question

A tube of length 1m is open on one end and closed on the other end. A sound source emitting at f = 440Hz (A-440) is moving towards the open end. Assume that the speed of sound is 343 m/s a.

a. Calculate the fundamental frequency associated with standing sound waves in the tube. What is the wavelength corresponding to this frequency?

b. What is the minimum speed that the sound source can be traveling towards the tube that will cause the sound wave reaching the tube to resonate with it(i.e. coincide with one of the allowed frequencies for standing waves in the tube) Which mode (i.e integer multiple of the fundamental frequency) is resonating?

Explanation / Answer

given

L = 1 m

f = 440 hz

v = 343 m/s

a) f1 = v/(4*L)

= 343/(4*1)

= 85.75 Hz

b) the given frequency is close to 5th harmonic

f5 = 5*f1

= 5*85.75

= 428.75 hz

let vs is the speed of sound source.

apply,

f' = f5*v/(v - vs)

v - vs = f5*v/f'

343 - vs = 428.75*343/440

vs = 343 - 428.75*343/440

= 8.8 m/s

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