Two tuning forks A and B are sounded together | vedclass

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(C) Let the frequency of tuning fork $A$ be $n_A$. Given the beat frequency is $6 \,Hz$ and $n_B = 384 \,Hz$,the possible frequencies for $A$ are $n_A

Vedclass · Accepted Answer

$390$

Vedclass · Answer

(C) Let the frequency of tuning fork $A$ be $n_A$. Given the beat frequency is $6 \,Hz$ and $n_B = 384 \,Hz$,the possible frequencies for $A$ are $n_A = 384 \pm 6$,which gives $390 \,Hz$ or $378 \,Hz$.When tuning fork $A$ is loaded with wax,its frequency decreases.If $n_A = 378 \,Hz$,loading it would decrease the frequency further (e.g.,to $376 \,Hz$),making the beat frequency $|384 - 376| = 8 \,Hz$,which contradicts the given condition that beats decrease to $4 \,Hz$.If $n_A = 390 \,Hz$,loading it decreases the frequency towards $384 \,Hz$. For the beat frequency to become $4 \,Hz$,the new frequency of $A$ must be $384 + 4 = 388 \,Hz$. Since the frequency decreased from $390 \,Hz$ to $388 \,Hz$ upon loading,this is consistent.Therefore,the original frequency of $A$ is $390 \,Hz$.

Two tuning forks $A$ and $B$ are sounded together and produce $6$ beats per second. The frequency of tuning fork $B$ is $384 \,Hz$. When tuning fork $A$ is loaded with wax,the number of beats per second becomes $4$. What is the frequency of tuning fork $A$ in $Hz$?

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