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 the 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 (`v_(B)`) were greater than that of A (`v_(A)`), further increase in `v_(B)` should have resulted in an increase in the beat frequency. But the beat frequency is found to decrease. this shows that `v_(B) lt v_(A)`. since `v_(A) - v_(B) = 5 Hz`, and `v_(A) = 427 Hz`, we get `v_(B) = 422 Hz`.