Two sitar strings A and B playing the note 'Ga' produce beats of frequency 6 Hz. The tension in stri

Question

Two sitar strings A and B playing the note 'Ga' produce beats of frequency 6 Hz. The tension in 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?

Professor PC Thomas Classes · Answer

Initial beat frequency is 6 Hz, so $f_B = 324 \pm 6$ Hz (318 Hz or 330 Hz). Reducing tension in A decreases $f_A$. If $f_B$ were 330 Hz, decreasing $f_A$ (e.g., to 321 Hz) would increase the beat frequency. Since the beat frequency decreases, $f_B$ must be below $f_A$. Thus, $f_B = 318$ Hz.