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. TI1e unknown frequency is
A. 250 Hz
B. 252 Hz
C. 254 Hz
D. 256 Hz

Answer 1

Correct Answer - C
Here,`upsilon_(A)=258Hz,upsilon_(B)=262Hz`
Let the frequency of unknown tuning fork be `upsilon`.
It produces `upsilon_(b) beats with A and `2upsilon_(b)` with B. Therefore,
`upsilon_(A)-upsilon=upsilon_(b)`….(i)
and `upsilon_(B)-upsilon=2upsilon_(b)`..(ii)
Subtract (i) from (ii), we get
`upsilon_(B)-upsilon_(A)=upsilon_(b)`
Substituting the given values, we get
`262-258=upsilon_(b)`
`upsilon_(b)=4 Hz`
From (i), `upsilon=upsilon_(A)-upsilon_(b)=(258-4)Hz=254 Hz`