Two tuning forks have frequencies 256 Hz (A) | vedclass

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(C) Let the frequency of the unknown tuning fork be $f$.The number of beats produced by $A$ $(256 \ Hz)$ and the unknown fork is $|f - 256|$.The numbe

Vedclass · Accepted Answer

$250$

Vedclass · Answer

(C) Let the frequency of the unknown tuning fork be $f$.The number of beats produced by $A$ $(256 \ Hz)$ and the unknown fork is $|f - 256|$.The number of beats produced by $B$ $(262 \ Hz)$ and the unknown fork is $|f - 262|$.According to the problem,the number of beats with $B$ is double the number of beats with $A$:$|f - 262| = 2 |f - 256|$.Case $1$: $f - 262 = 2(f - 256)$$f - 262 = 2f - 512$$f = 512 - 262 = 250 \ Hz$.Case $2$: $f - 262 = -2(f - 256)$$f - 262 = -2f + 512$$3f = 774$$f = 258 \ Hz$.Checking the options,$250 \ Hz$ is provided as option $C$.

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