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

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

AFMCAFMC 2008Electromagnetic Waves

Solution:

To have 4 beats per second, $f _{ A }$ can be either $316 Hz$ or $324 Hz$.
Since filing increases the frequency, beat frequency, $f=f_{B}-f_{A}=4$ beats per second
$f _{ A }=$ frequency of fork $A$ before filing
$f _{ A }=320-4=316 Hz$