A 80.0 cm wire of mass 9.20 g is tied at both ends and adjusted to a tension of

Question

A 80.0 cm wire of mass 9.20 g is tied at both ends and adjusted to a tension of 38.0 N .

Part A

When it is vibrating in its second overtone, find the frequency at which it is vibrating.

Part B

When it is vibrating in its second overtone, find the wavelength at which it is vibrating.

Part C

When it is vibrating in its second overtone, find the frequency of the sound waves it is producing.

Part D

When it is vibrating in its second overtone, find the wavelength of the sound waves it is producing.

Please show step by step.

Explanation / Answer

Given,

Length of wire, l = 0.8 m

Mass, m = 9.2 g

Tension, T = 38 N

A)

for second overtone,

f = (3/2L) sqrt(T/u)

f = (3/(2 x 0.8)) sqrt(38/(0.0115))

f = 107.78 Hz

B)

wavelength, lambda = 2L/3 = 2 x 0.8 /3 = 0.53 m

C)

f = 107.78 Hz

D)

speed of sound wave = 343 m/s

wavelength = speed /f = 343 /107.78 = 3.18 m

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