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Question

In a resonance tube the first resonance with a tuning fork occurs at 16 cm and second at 49 cm. If the velocity of sound is 330 m/s, the frequency of tuning fork is :

A
500
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B
300
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C
330
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D
165
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Solution

The correct option is A 500
Let the resonance column has the end correction to be x.

Length of the air column for first resonance to occur l1=16cm=0.16 m

Using for Ist resonance l1+x=λ4

Length of the air column for second resonance to occur l2=49cm=0.49 m

For second resonance l2+x=3λ4

l2l1=λ2

0.490.16=λ2 λ=0.66 m

From v=νλ, we get 330=ν×0.66
ν=500 Hz

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