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, fA = 324 Hz
Frequency of string B = fB
Beat’s frequency, n = 6 Hz
beat's frequency is given as :
$n=|f_A±f_B|$
$6=324±f_B$
$f_B=330\, Hz \,or \,318\, Hz$
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:
$v∝√T$
Hence the beat frequency cannot be 330 Hz
$∴f_B=318 Hz$