Question

Two sitar strings, $A$ and $B$, playing the note ‘Dha’ are slightly out of tune and produce beats of frequency $5Hz$. The tension of the string $B$ is slightly increased and the beat frequency is found to decrease by $3Hz$. If the frequency of $A$ is $425Hz$, the original frequency of $B$ is :

• A. 430 Hz
• B. 420 Hz
• C. 428 Hz
• D. 422 Hz

Answer 1

Answer: (B)

Frequency of sitar string A, $f_1=425Hz$.
Frequency of sitar string $B,f_2=(425\pm 5)Hz$,
that is, either $420Hz$ or $430Hz$.
On increasing tension in string $B$, its frequency will increase as $n\propto \sqrt{T}$, where $T$ is tension.
If $430Hz$ is correct, then on increasing tension number of beats should have increased.
But, the number of beats has decreased. It means $420Hz$ is correct.
On increasing tension, frequency increases from $420Hz$ to $422Hz$ and number of beats is 3.