Question

A tuning fork of known frequency 256Hz 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 increase. 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 : A tuning fork of known frequency 256Hz 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 increase. The frequency of the piano string before increasing the tension was:

Solution :

Frequency of Piano = $(256\pm 5)Hz$

We know that $F=\frac{V}{\lambda }$ and $V=\sqrt{\frac{T}{\mu }}$ where T is Tension

When T $\uparrow$ then F $\uparrow$

And Beat frequency deacreases this can happen only when Piano frequency is (256 - 5)Hz

The Correct Opt : C