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(C) Let the two tuning forks be $A$ and $B$ with frequencies $n_A = 256 \, Hz$ (known) and $n_B$ (unknown). The beat frequency is $x = 4 \, bps$.The p

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$260$

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(C) Let the two tuning forks be $A$ and $B$ with frequencies $n_A = 256 \, Hz$ (known) and $n_B$ (unknown). The beat frequency is $x = 4 \, bps$.The possible frequencies for the unknown tuning fork are $n_B = 256 + 4 = 260 \, Hz$ or $n_B = 256 - 4 = 252 \, Hz$.It is given that when the fork $A$ (frequency $256 \, Hz$) is loaded with wax,its frequency decreases $(n_A \downarrow)$. Consequently,the beat frequency increases.If $n_B = 252 \, Hz$,then $n_A - n_B = 256 - 252 = 4 \, Hz$. When $n_A$ decreases,the difference $(n_A - n_B)$ decreases,meaning the beat frequency would decrease.If $n_B = 260 \, Hz$,then $n_B - n_A = 260 - 256 = 4 \, Hz$. When $n_A$ decreases,the difference $(n_B - n_A)$ increases,meaning the beat frequency increases.Since the problem states that the beat frequency increases,the correct frequency of the other fork must be $n_B = 260 \, Hz$.

Two tuning forks when sounded together produce $4$ beats/sec. The frequency of one fork is $256 \, Hz$. The number of beats heard increases when the fork of frequency $256 \, Hz$ is loaded with wax. The frequency of the other fork is (in $, Hz$)

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