A tuning fork of known frequency 256 Hz makes 5 beats per second with the vibrating string of a pian

Question

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\

Professor PC Thomas Classes · Answer

(c) : The possible frequencies of piano are $(256+5) \mathrm{Hz}$ and $(256-5) \mathrm{Hz}$.\ For piano string, $v=\frac{1}{2 l} \sqrt{\frac{T}{\mu}}$\ When tension $T$ increases, $v$ increases\ (i) If 261 Hz increases, beats/sec increase. This is not given in the question.\ (ii) If 251 Hz increases due to tension, beats per second decrease. This is given in the question.\ Hence frequency of piano $=(256-5) \mathrm{Hz}$.\