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

The frequency of vibration of a sonometer wire is given by:

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

Calculating for initial tension:

$f_1 = \frac{1}{2} \sqrt{\frac{6}{\mu}}$

Calculating for new tension:

$f_2 = \frac{1}{2} \sqrt{\frac{54}{\mu}}$

Given:

$f_2 - f_1 = 12$

Ratio of frequencies:

$\frac{f_1}{f_2} = \frac{1}{3}$

Substituting values:

$f_1 = 6 \, \text{Hz}$