On sounding tuning fork A with another tuning | vedclass

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(D) Let the frequency of tuning fork $A$ be $n_A$ and the frequency of tuning fork $B$ be $n_B = 384 \ Hz$.The initial beat frequency is $x_1 = |n_A -

Vedclass · Accepted Answer

$390$

Vedclass · Answer

(D) Let the frequency of tuning fork $A$ be $n_A$ and the frequency of tuning fork $B$ be $n_B = 384 \ Hz$.The initial beat frequency is $x_1 = |n_A - n_B| = 6 \ Hz$.This implies $n_A = 384 \pm 6$,so $n_A$ is either $390 \ Hz$ or $378 \ Hz$.When tuning fork $A$ is loaded with wax,its frequency $n_A$ decreases.After loading,the new beat frequency is $x_2 = 4 \ Hz$.If $n_A = 390 \ Hz$,loading decreases it towards $384 \ Hz$,so the beat frequency decreases from $6$ to $4$. This matches the given condition.If $n_A = 378 \ Hz$,loading decreases it further away from $384 \ Hz$,so the beat frequency would increase from $6$ to a higher value. This contradicts the given condition.Therefore,the original frequency of tuning fork $A$ is $390 \ Hz$.

On sounding tuning fork $A$ with another tuning fork $B$ of frequency $384 \ Hz$,$6$ beats are produced per second. After loading the prongs of $A$ with some wax and then sounding it again with $B$,$4$ beats are produced per second. What is the frequency of the tuning fork $A$ in $Hz$?

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