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 is found to decrease to 3 Hz. What is the original frequency of B, if the frequency of A is 427 Hz?

Explanation

Increase in the tension of a string increases its frequency. If the original frequency of B ( ν B) were greater than that of `A ( ν_(A) )`, further increase in `ν_(B)` should have resulted in an increase in the beat frequency. But the beat frequency is found to decrease. This shows that `ν_(B) lt ν_(A)`. Since `ν_(A) – ν_(B) = 5 Hz`, and `ν_(A) = 427 Hz`, we get `ν_(B) = 422 Hz`