Question

A tuning fork vibrating with sonometer, having tension in the wire as T, produces 4 beats per sec. The beat frequency does not change when tension in the wire changes to 1.21T. Find the frequency of the tuning fork (assuming that the sonometer wire is vibrating in the same mode in both cases).

• A. 80 Hz
• B. 84 Hz
• C. 88 Hz
• D. 76 Hz

Answer 1

The correct option is B 84 Hz

Let frequency of tuning fork be $f_T$ .
$f_T-f=4\dots \left(1\right)$
$f^{\prime }–f_T=4\dots \left(2\right)$
Wkt, $f=\frac{n}{2L}\sqrt{\frac{T}{\mu }}$
$f^{\prime }=\frac{n}{2L}\sqrt{\frac{1.21T}{\mu }}$
$\Rightarrow \frac{f^{\prime }}{f}=\sqrt{1.21}=1.1....\left(3\right)$
From (1) ,(2) and (3)
$1.1f-f_T=4$
$\frac{-f_T+1.1f=4}{0.1f=8}$
$f=80Hz$
Put the value of f in equation (1),
$f_T-80=4$
$f_T=80+4$
$f_T=84\text{Hz}$