Question

Two tuning forks, $A$ and $B$, produce notes of frequencies $258Hz$ and $262Hz$. 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. $250Hz$
• B. $252Hz$
• C. $254Hz$
• D. $256Hz$

Answer 1

Answer: (C)

$254Hz$

Here, ${\upsilon }_A=258Hz,{\upsilon }_B=262Hz$
Let the frequency of unknown turning fork be $\upsilon$.
It produces ${\upsilon }_b$ beats with $A$ and $2{\upsilon }_b$ with $B$. Therefore,
${\upsilon }_A-\upsilon ={\upsilon }_b$ ......(i)
and ${\upsilon }_B-\upsilon =2{\upsilon }_b$ ......(ii)
Subtract (i) from (ii), we get
${\upsilon }_B-{\upsilon }_A={\upsilon }_b$
Substituting the giving values, we get
$262-258={\upsilon }_b$
${\upsilon }_b=4Hz$
From (i), $\upsilon ={\upsilon }_A-{\upsilon }_b=(258-4)Hz=254Hz$