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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
  1. vibrate with a frequency of 208 Hz

  2. vibrate with a frequency of 832 Hz

  3. stop vibrating.

  4. vibrate with a frequency of 416 Hz


Solution

The correct option is D

vibrate with a frequency of 416 Hz


When the length is doubled keeping other things constant, the fundamental frequency must be halved  asf α 1L 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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