Two tuning forks A and B produce notes of fre | vedclass

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Question

(C) Let the unknown frequency be $f$.The beat frequency with $A$ $(256 \ Hz)$ is $|f - 256|$.The beat frequency with $B$ $(262 \ Hz)$ is $|f - 262|$.A

Vedclass · Accepted Answer

$250$

Vedclass · Answer

(C) Let the unknown frequency be $f$.The beat frequency with $A$ $(256 \ Hz)$ is $|f - 256|$.The beat frequency with $B$ $(262 \ Hz)$ is $|f - 262|$.According to the problem,the beat frequency with $B$ is twice the beat frequency 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 condition: The beat frequency with $B$ is twice that with $A$. If $f = 250$,beats with $A = |250 - 256| = 6$,beats with $B = |250 - 262| = 12$. Since $12 = 2 	imes 6$,$250 \ Hz$ is a valid solution.

Two tuning forks $A$ and $B$ produce notes of frequencies $256 \ Hz$ and $262 \ Hz$ respectively. An unknown note sounded at the same time as $A$ produces beats. When the same note is sounded with $B$,the beat frequency is twice as large. The unknown frequency could be ... $Hz$

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