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  4. A tuning fork of known frequency 256 Hz 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

Q. A tuning fork of known frequency 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

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Solution:

The possible frequencies of piano are
and
image
For piano string,
When tension increases, increases
(i) If increases, beats/sec increase. This is not given in the question.
(ii) If increases due to tension, beats per second decrease. This is given in the question.
Hence frequency of piano