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  4. Two tuning forks, A and B, produce notes of frequencies 258 Hz and 262 Hz. An unknown note sounded with A produces certain beats. When the same note is sounded with B, the beat frequency gets doubled. The unknown frequency is

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Q. Two tuning forks, $A$ and $B$, produce notes of frequencies $258 \,Hz$ and $262\, Hz$. An unknown note sounded with $A$ produces certain beats. When the same note is sounded with $B$, the beat frequency gets doubled. The unknown frequency is

KCETKCET 2011Waves

Solution:

Given, $n_{A}=258\, Hz,\, n_{B}=262\, Hz$
If it produces $x$ beats with 258 and $2 x$ with $262 .$
$262-(258-x) =2 x $
$262-258+x =2 x $
$x =4$
$n =254\, Hz$