Question

A $70cm$ long sonometer wire is in unison with a tuning fork. If the length of the wire is decreased by $1.0cm$, it produces $4$ beats per second with the same tuning fork. The frequency of the tuning fork is

• A. 186 Hz
• B. 220 Hz
• C. 276 Hz
• D. 312 Hz

Answer 1

Answer: (C)

Let the frequency of the fork be $n$.
In the first case, the length of the wire is $70cm$.
Therefore, $n=\frac{1}{2\times 70}\sqrt{\frac{T}{m}}\dots$ (i)
On decreasing the length of the wire, its frequency will increase.
Hence, in the second case when the length is $69cm$,
then $n+4=\frac{1}{2\times 69}\sqrt{\frac{T}{m}}\dots$ (ii)
Dividing Eqs. (i) by (ii), we get
$\frac{n}{n+4}=\frac{1/70}{1/69}$
$\Rightarrow \frac{n}{n+4}=\frac{69}{70}$
$70n-69n=69\times 4$
$n=276Hz$