Physics Question on Waves

Question

A tuning fork $A$ produces $4$ beats per second with another tuning fork $B$ of frequency $320\, Hz$ . On filing one of the prongs of $A, 4$ beats per second are again heard when sounded with the same fork $B$ . Then the frequency of the fork $A$ before filing is

Answer 1

Solution

There are 4 beats between $A$ and $B$ , therefore the possible frequencies of A are $316$ or $324$ that is $(320 � 4) \,Hz$ When the prong of A is filed, its frequency becomes greater than the original frequency. If we assume that original frequency of A is 324 then on filing its frequency will be greater then 324. The beats between A and B will be more than 4. But it is given that the beats are again 4, therefore, 324 is not possible. Therefore, required frequency must be 316 Hz. (This is true, because on filing the frequency may increase so as to give 4 beats with B of frequency 320 Hz)