Two sitar strings A and B playing the note 'Dha' are slightly out of tune and produce beats of frequ

Question

Two sitar strings A and B playing the note 'Dha' are slightly out of tune and produce beats of frequency 5 Hz. The tension of string B is slightly increased, and the beat frequency decreases to 3 Hz. What was the original frequency of B if the frequency of A is 427 Hz?

Professor PC Thomas Classes · Answer

Beat frequency = $|f_A - f_B| = 5$ Hz. So, $f_B$ could be 432 Hz or 422 Hz. Increasing the tension of B increases $f_B$. If $f_B$ was 422, an increase would bring it closer to 427, reducing the beat frequency (matching the observation). Thus, original $f_B = 422$ Hz.