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String Fixed at Both Ends

A tuning fork...

Question

A tuning fork of frequency 512 Hz is vibrated with a sonometer wire and 6 beats per second are heard. The beat frequency reduces if the tension in the string is slightly increased. The original frequency of vibration of the string is
(a) 506 Hz
(b) 512 Hz
(c) 518 Hz
(d) 524 Hz.

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Solution

a) 506 Hz

The frequency of the sonometer may be 512 ± 6Hz, i.e., 506 Hz or 518 Hz.
On increasing the tension in a sonometer wire, the velocity of the wave (v) increases proportionately as the number of beats decreases. Therefore, the frequency of the sonometer wire is 506 Hz.

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