Question

A tuning fork resonates with a sonometer wire of length 1 m stretched with a tension of 6 N. When the tension in the wire is changed to 54 N, the same tuning fork produces 12 beats per second with it. The frequency of the tuning fork is _______ Hz.

Answer 1

Correct Answer: 6

The formula for the vibration frequency of a sonometer wire is:

\(f = \frac{1}{2L} \sqrt{\frac{T}{\mu}}\)

For the initial tension:

\(f_1 = \frac{1}{2} \sqrt{\frac{6}{\mu}}\)

For the new tension:

\(f_2 = \frac{1}{2} \sqrt{\frac{54}{\mu}}\)

It is given that:

\(f_2 - f_1 = 12\)

The ratio of the frequencies is:

\(\frac{f_1}{f_2} = \frac{1}{3}\)

Upon substitution:

\(f_1 = 6 \, \text{Hz}\)