A tuning fork of known frequency 256 Hz makes 5 beats/s with the vibrating string of a piano. The beat frequency decreases to 2 beats/s when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was

Question

Dr. Abubacker · Accepted Answer

(c) $v_{1} = 256\ Hz$
For tuning for $v_{1} - v_{1} = \pm 5,$
$v_{2} = frequency\ of\ piano$
$v_{2} = (256 + 5)Hz\ or\ (256 - 5)Hz$
When tension is increased, the bear frequency decreases to 2 beats/s.
If we assume that the frequency of piano string is 261 Hz, then on increasing tension, frequency, more than 261 Hz. But it is given that beat frequency decreases to 2, therefore, 261 is not possible.
Hence, 251 Hz i.e., 256-5 was the frequency of piano string before increasing tension.

Q. A tuning fork of known frequency 256 Hz makes 5 beats/s with the vibrating string of a piano. The beat frequency decreases to 2 beats/s when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was

Explanation

Reviewed by Dr. Abubacker

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