Question

A tuning fork vibrating with a sonometer having $20cm$ wire produces $5$ beats/s. The beat frequency does not change when the length of the wire is changed to $21cm$. The frequency of tuning fork is :

• A. 200
• B. 210
• C. 205
• D. 215

Answer 1

Answer: (C)

The frequency of sonometer wire is given by
$n=\frac{1}{2l}\sqrt{\frac{T}{m}}$
where $l$ is length,
$T$ the tension
and $m$ the mass per unit length.
When the length of wire is $0.20m$.
$n_1=\frac{1}{2\times 0.2}\sqrt{\frac{T}{m}}$
When length is $0.21m$,
then $n_2=\frac{1}{0.21\times 2}\sqrt{\frac{T}{m}}$
Let frequency of tuning fork be $N$,
$\frac{n_1}{n_2}=\frac{N+5}{N-5}$
$\Rightarrow \frac{0.21}{0.20}=\frac{N+5}{N-5}$
$\Rightarrow$ $0.21N-1.05=0.2N+1$
$\Rightarrow 0.01N=2.05$
$\Rightarrow$ $N=\frac{2.05}{0.01}=205Hz$