Question

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

• A. $250\, Hz$
• B. $252\, Hz$
• C. $254\, Hz$
• D. $256\, Hz$

Answer 1

Answer: (C)

$254\, Hz$

Answer 2

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