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Question

A string (fixed at both ends) of length 1 m has the mass per unit length 0.1 g cm1. What would be the frequency of vibration of this string for third overtone under the tension of 400 N ?

A
400 Hz
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B
300 Hz
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C
50 Hz
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D
200 Hz
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Solution

The correct option is A 400 Hz
Mass per unit length of string.
μ=0.1 g/cm=0.1×103102=0.01 kg/m
speed of wave is,
v=Tμ=4000.01=200 m/s
frequency of vibration for string fixed at both ends.
fx=nv2L
For 3rd overtone, n=4(4thharmonic)
f4=4×2002×1=400 Hz

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