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(C) Let the frequency of tuning fork $A$ be $n_A$ and the frequency of tuning fork $B$ be $n_B = 256 \ Hz$.The beat frequency is given as $x = 3 \ Hz$

Vedclass · Accepted Answer

$259$

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(C) Let the frequency of tuning fork $A$ be $n_A$ and the frequency of tuning fork $B$ be $n_B = 256 \ Hz$.The beat frequency is given as $x = 3 \ Hz$.Therefore,$n_A = n_B \pm x = 256 \pm 3$,which means $n_A$ is either $259 \ Hz$ or $253 \ Hz$.When tuning fork $A$ is loaded with wax,its frequency $n_A$ decreases.Case $1$: If $n_A = 253 \ Hz$,loading it will decrease the frequency further below $253 \ Hz$. The new beat frequency would be $256 - n_A' > 3$,which contradicts the observation that the beat frequency remains $3 \ Hz$.Case $2$: If $n_A = 259 \ Hz$,loading it will decrease the frequency towards $256 \ Hz$. The new beat frequency would be $n_A' - 256 = 3$,which is consistent with the observation.Thus,the original frequency of tuning fork $A$ is $259 \ Hz$.

When a tuning fork $A$ of unknown frequency is sounded with another tuning fork $B$ of frequency $256 \ Hz$,then $3$ beats per second are observed. After that,$A$ is loaded with wax and sounded again,and $3$ beats per second are observed. The frequency of the tuning fork $A$ is ..... $Hz$.

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