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

it is given that ,
frequency of string A , $f_A$=324Hz
Beats frequency , n = 6Hz
let the frequency of string B is $f_B$

we know, Beats frequency is given as,
$n=|f_A\pm f_B|$
6 = 324 ± $f_B$
so, $f_B$ = 318 Hz or 330 Hz

frequency decreases with a decrease in the tension in a string because we know, frequency is directly proportional to square root of tension.e.g., $f\propto\sqrt{T}$
hence, the frequency of string B ≠ 330 Hz
so, frequency of string B = 318Hz