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 :

• A. (256 + 2) Hz
• B. (256 - 2) Hz
• C. (256 - 5) Hz
• D. (256 + 5) Hz

Answer 1

Answer: (C)

(256 - 5) Hz

Given : beat frequency = 5 beats per second

Thus frequency of the piano string can either be $(256-5)Hz$ OR $(256+5)Hz.$

Also, as $\nu \propto v$ where $v=\sqrt{\frac{T}{\mu }}$

Thus $\nu \propto \sqrt{T}⟹$ frequency increases with increase in tension.

Now if the frequency of the piano string would be $(256+5)Hz$ earlier, then due to inrease in tension the value of frequency rises further which in result increases the beat frequency. But according to the question, beat frequency must decrease.

Hence, frequency of the piano string before increasing the tension was $(256-5)Hz$