Question

A tuning fork vibrating with a sonometer having $20cm$ wire produces $5$ beats per second. If the beat frequency does not change if the length of the wire is changed to $21cm$, then the frequency of the tuning fork $($in $Hz)$ must be

• A. $200$
• B. $210$
• C. $205$
• D. $215$

Answer 1

The correct option is C $205$

Let $f_t$ be the frequency of the tuning fork.

Then, frequency of $21cm$ sonometer $=$ $f_t-5$
and frequency of $20cm$ sonometer $=$ $f_t+5$

Frequency of sonometer vibration $f=\frac{v}{2L}$

$f_t-5=\frac{v}{2\times 21}$

$f_t+5=\frac{v}{2\times 20}$

$($since $v$ is going to remain constant for the same sonometer material$)$

Hence,

$2(f_t+5)20=2(f_t-5)21$
$20f_t+100=21f_t-105$
$f_t=205Hz$.