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Two tuning forks x and y produce tones of frequencies 256 Hz and 262 Hz respectively. An unknown tone sounded with x produces, beats. When it is sounded with y the number of beats produced is doubled. The unknown frequency is

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254Hz

250Hz

264Hz

259Hz

answer is B.

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Detailed Solution

Let the number of beats heard with 'x' is 'P'. If n be the unknown frequency, then

$\large n\,\, = 256 + P,256 - P - - - (1)$

The number of beats produced is doubled with 'y' then

n = 262+2P, 262-2P -----(1)

From the above two cases, it is clear that

(262-2P) = (256-P)

$\large \Rightarrow \,P\, = \,6$

$\large \therefore$ Unkown frequency = (256-6)Hz = 250 Hz

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