## Question

A tuning fork of frequency 480 Hz produces 10 beats per second when sounded with a vibrating sonometer string. What must have been the frequency of the string if a slight increase in the tension of the string produces fewer beats per second than before?

### Solution

470 Hz

The frequency of the string is either *V*_{1} = 480 – 10 = 470 Hz or *V*_{2} = 480 + 10 = 490 Hz. Now, the frequency of wire ∝ So, when tension is slightly increased, the frequency of the wire also slightly increases. Hence fewer beats will be produced if the frequency of the wire is 470 Hz.

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