Two sitar strings $A$ and $B$ playing the note $'Ga'$ are slightly out of tune and produce beats of frequency $6\,Hz$ . The tension in the string $A$ is slightly reduced and the beat frequency is found to reduce to $3\,Hz$. If the original frequency of $A$ is $324\,Hz$, what is the frequency of $B$ ..... $Hz$
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Frequency of string $\mathrm{A}, f_{A}=324 \mathrm{H} z$
Frequency of string $B=f_{B}$
Beat's frequency, $n=6 H z$
Beat's Frequency is given as$:$
$n=\left|f_{A}-f_{B}\right|$
$6=\left|324-f_{B}\right|$
$f_{B}=330 H z$ or $318 H z$
Frequency decreases with a decrease in the tension in a string. This is because frequency is directly proportional to the square root of tension. It is given as$:$
$f \propto \sqrt{T}$
Hence, the beat frequency cannot be $330 \mathrm{Hz}$
$\therefore f_{B}=318 H z$
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