Question

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 ?

Answer 1

Frequency of string A, $f_A=324Hz$
Frequency of string $B=f_B$
Beat’s frequency, $n=6Hz$
Beat's Frequency is given as:

$n=|f_A-f_B|$

$6=|324-f_B|$

$f_B=330Hz$ or $318Hz$

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 Hz

$\therefore f_B=318Hz$