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Question

If the frequency of the 2nd and 5th harmonics of string fixed at both ends differ by 108 Hz. What is the fundamental frequency of the string?

A
18 Hz
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B
9 Hz
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C
36 Hz
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D
72 Hz
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Solution

The correct option is C 36 Hz
Frequency of vibration in a string fixed at both ends is given by
f=nv2L
Fundamental frequency f=v2L
For second harmonic, f2=2v2L=2f
For fifth harmonic, f5=5v2L=5f

From the data given in the question,
5f2f=1083f=108
f=36 Hz

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