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Question

In a resonance tube with tuning fork of frequency, 512Hz, first resonance occurs at water level equal to 30.3 cm and second resonance occurs at 63.7 cm. The maximum possible error in the speed of sound is

A
51.2cm/s
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B
102.4cm/s
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C
204.8cm/s
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D
153.6cm/s
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Solution

The correct option is C 204.8cm/s
We can write two equations:

l1+e=v4f and l2+e=3v4f

Now, l2l1=2v4f=v2f

Differentiate, (l2l1)l2l1=vv

v=(l2l1)vl2l1=(l2l1)(2f)

To maximize error,
v=(l1+l2)(2f)=2×512(0.1+0.1)=2×512×0.2=204.8cm/s

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