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Two sitar strings A and B playing the n...

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 ?

Text Solution

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Suppose original frequencies of wires A and B are respectively `f _(A) and f _(B).`
Here `f _(A) = 427 Hz and `initially `f _(B) = 422 Hz or f _(B) = 432 Hz` (Because initially there are 5 beats per second between A and B).
Now, after increasing tension in B, its frequency increases and assumes such a value `f._(B)` which can produce 3 beats per second with A. Hence, we should take `f _(B)= 422 Hz and f ._(B) = 424 Hz.` So that `f._(B) gt f_(B)`
`f _(A) -f_(B) =427-422 =5` beats per second
(before increasing tension in B)
`f _(A) - f._(B) =427 -424=4`
(After increasing tension in B)
Note: Here we can not take `f _(B) = 432 Hz` because after increasing tension in B its frequency would be greater than 432 Hz and then it would peoduce more than 5 beats per second with A which would be wrong as per the statement.
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