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Question

A string of length 10 cm fixed at one end and free at another end, has its fundamental frequency half that of second overtone for another string fixed at both ends. What will be the length of string fixed at both ends?
(Assume velocity of wave in both strings is same)

A
10 cm
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B
20 cm
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C
40 cm
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D
30 cm
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Solution

The correct option is D 30 cm
For a string fixed at one end and free at another end, fundamental mode
f0=V4L
f0=V4×0.1=V0.4
For the 2nd overtone of string (fixed at both ends)
f2=3V2l
Given f0=f22V0.4=3V2l×2
l=0.3 m=30 cm

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