A tuning fork A of unknown frequency produces 5 beats/s with a fork of known frequency 340Hz. When fork A is filed, the beat frequency decreases to 2beat/s. What is the frequency of fork A ?

${\text{Let say f}}_A=f and f_B=340 ,$

$\text{A and B produces 5 beats.}$

${\text{So, either f}}_1=340+5=345 Hz$

or

$f_2=340-5=335 Hz$

$\text{When fork A if filed, its frequency increases, by 3 Hz (assume).}$

$\text{So, new frequency of fork A is}$

${\text{either f}}_1\text{'} =340+3=343 Hz$

$or f_2\text{'} =335+3=338 Hz$

$$\begin{gathered} \text{As per question , the new frequency of A should have beat frequency of 2 beat/s with B.} \\ {\text{This is satisfied by f}}_2\text{'}. \end{gathered}$$

${\text{Hence, original frequency of fork A is f}}_2=335 Hz$