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String Fixed at Both Ends

A sonometer w...

Question

A sonometer wire of length l vibrates in fundamental mode when excited by a tuning fork of frequency 416 Hz. If the length is doubled keeping other things same, the string will

A

vibrate with a frequency of 416 Hz

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B

vibrate with a frequency of 208 Hz

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C

vibrate with a frequency of 832 Hz

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D

stop vibrating.

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Solution

The correct option is A vibrate with a frequency of 416 Hz
When the length is doubled keeping other things constant, the fundamental frequency must be halved $a s f α \frac{1}{L}$ But the tuning fork is still vibrating with 416 Hz, which will be the second harmonic of the string. String will vibrate with this frequency only.

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