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Two tuning forks A and B produce notes of frequencies 258 Hz and 262 Hz. An unknown note sounded with A produces certain beats. When the same note is sounded with B, the beat frequency gets doubled. The unknown frequency is

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250 Hz

254 Hz

252 Hz

245 Hz

answer is C.

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Detailed Solution

Given, $n_{A} = 258 Hz and n_{B} = 262 Hz$

If it produces x beats with 258 and 2x with 262, then

262 $-$ (258 $-$ x) = 2x
$\Rightarrow$ 262 $-$ 258 + x = 2x $\Rightarrow$ x = 4
Therefore, unknown frequency, n = 258 $-$ x = 254 Hz

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