Please show all work and specify the correct answer at the bottom. Do not put do

Question

Please show all work and specify the correct answer at the bottom. Do not put down an answer that is not one of the choices.

A heavy stone of mass m is hung from the ceiling by a thin 8.25-g wire that is 65.0 cm long. When you gently pluck the upper end of the wire, a pulse travels down the wire and returns 7.84 ms later, having reflected off the lower end. The speed of sound in the room is 344 m/s, and the stone is heavy enough to prevent the lower end of the wire from moving. If the wire is vibrating in its second overtone, what is the frequency of the sound it will produce?

Explanation / Answer

383 Hz is the correct answer.

given

L = 65 cm = 0.65 m

t = 7.84 ms

from the given data speed of the wave on string, v = 2*L/t

= 2*0.65/(7.84*10^-3)

= 165.8 m/s

second overtone or third harmonic, f3 = 3*v/(2*L)

= 3*165.8/(2*0.65)

= 383 hz

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