Question

A sono meter wire is in unison with a tuning fork. When its length increases by 4% it gives 8 beats/s with the same fork. The frequency of the fork is:

• A. 196 Hz
• B. 200 Hz
• C. 204 Hz
• D. 208 Hz

Answer 1

The correct option is B 200 Hz

Solution

Let the initial frequency of sonometer

(or for k) be f and change in frequency

of sonometer wire be $\Delta f$. Then,

We know,

$f=\frac{1}{2}l\sqrt{\frac{I}{m}}$, frequency of wire

$\Rightarrow \frac{\Delta f}{f}=\frac{-\Delta l}{l}-\frac{\Delta m}{2m}+\frac{\Delta T}{2T}$

As $\frac{\Delta l}{l}=\frac{4}{100},\Delta m=0$ and $\Delta T=0$

$\Rightarrow \frac{\Delta f}{f}=\frac{-4}{100}$

It is given that,

Beats = $\left|\Delta f\right|=8$ Hz. so,

$\Delta f=-8Hz$

$\Rightarrow \frac{-8}{f}=\frac{-4}{100}\Rightarrow f=200Hz$

Initial frequency of sonometer wire

and for k is 200 Hz

Option - B is correct.