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
• B. vibrate with a frequency of 208 Hz
• C. vibrate with a frequency of 832 Hz
• D. stop vibrating.

Answer 1

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 $asf\alpha \frac{1}{L}$ 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.