Question

# A tuning fork of frequency 280 Hz produces 10 beats per sec when sounded with a vibrating sonometer string. When the tension in the string increases slightly, it produces 11 beats per sec. The original frequency of the vibrating sonometer string is :

A
269 Hz
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B
291 Hz
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C
270 Hz
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D
290 Hz
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Solution

## The correct option is C 270 HzLet,The frequency of tuning fork is νT=280HzThe frequency of the sonometer string is νsThe frequency of beats is|νT−νs|=10Hence, the frequency of sonometer string is either 10Hz more i.e. 290Hz or 10Hz less i.e. 270Hz because the increase in this frequency will reduce the frequency of beats.But when tension is applied to the string its frequency increases and the number of beats also increases. Hence, the frequency of string cannot be 290Hz.Therefore the frequency of the sonometer string is 270Hz.

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