Question

An unknown tunning fork sounded together with a tunning fork of frquency 256 emits two beats.On loading tunning fork of frquency 256, the number of beats heard is 1 per second.The frquency of unknown tunning fork is

• A. 257
• B. 258
• C. 256
• D. 254

Answer 1

The correct option is D 254

Given are two tuning forks, one with $\nu =256$ and the other is unknown.

Let's suppose that the frequency of the unknown tuning fork is ${\nu }_{unknown}$

We know that beat frequency is the difference of the two individual frequencies

So

${\nu }_{beat}=|{\nu }_{unknown}-256|$

This value is given to be 2 initially.

So,

$|{\nu }_{unknown}-256|=2$

When a tuning fork is loaded its frequency decreases

So the frequency of the known tuning fork becomes smaller

than 256.

The new ${\nu }_{newbeat}$ is 1 which is smaller than the old ${\nu }_{beat}$

This suggests that ${\nu }_{unknown}$ was smaller than 256 earlier and

after the tuning fork was loaded its frequency decreased

and came more close to ${\nu }_{unknown}$

Hence, ${\nu }_{unknown}=256-v_{beat}=256-2=254$

So D is the correct answer.