Question

A tuning fork produces $4$ beats per second, with another tuning fork of frequency $256\text{Hz}$. The first one is now loaded with a little wax and the beat frequency is found to increase to $6$ per second. The original frequency $\left(\text{in Hz}\right)$ of the tuning fork was _____.

Answer 1

Let the frequency of the first tuning fork be $x$.

Beat frequency is given by,

$\Delta f=|f_1-f_2|$

Since the beat frequency is $4$

So, $x=256+4\text{or}256-4$

$\therefore x=260\text{Hz}\text{or}252\text{Hz}$

After the loading of the wax, the frequency of the first tuning fork will decrease.

Since, after loading of the wax, beat frequency is found to increase, so original frequency should be less than $256\text{Hz}$.

$\therefore x=252\text{Hz}$

Hence, $252$ will be the correct answer.