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

Here, frequency of string A, `v_(A)=427Hz`, beat frequency v=5Hz
Say frequency of string `B=v_(B)`
As `v=|v_(A)-v_(B)|implies v_(B)=v_(A)+-v`
`therefore v_(B)=427+-5Hz," "v_(B)=432 or 422Hz`.
Increase in tension in string increase its frequency
Here beat frequency is decreased, therefore `v_(B) lt v_(A)`. so original frequency of B is 422Hz.