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 = 6 Hz
Beat's frequency is given as:
$n=|f_A\pm f_B|6=324\pm f_B{f}_B=330Hzor318Hz$
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:
$v\propto \sqrt{T}$
Hence, the beat frequency cannot be 330 Hz.
$\therefore f_B=318Hz$