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Question

A tuning fork of known frequency $256 H z$ makes $5$ beats per second with the vibrating string of a piano. The beat frequency decreases to $2$ beats per second when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was-

A

(256 + 2) H z

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B

(256 - 2) H z

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C

(256 - 5) H z

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D

(256 + 5) H z

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Solution

The correct option is C $(256 - 5) H z$
$f = \frac{1}{2 l} \sqrt{\frac{T}{m}}$
$2 = 256 - \frac{1}{2 l} \sqrt{\frac{T_{2}}{m}}$
$5 = 256 - \frac{1}{r 2 l} \sqrt{\frac{T_{1}}{m}} \Rightarrow f_{P} = (256 - 5) H z .$

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