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An air column in a tube $32 c m$ long, closed at one end, is in resonance with a tuning fork. The air column in another tube, open at both ends, of length $66 c m$ is in resonance with another tuning fork. When these two tuning forks are sounded together, they produce 8 beats per second. Then the frequencies of the two tuning forks are, (Consider fundamental frequencies only).

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$250 H z, 258 H z$

$240 H z, 248 H z$

$264 H z, 256 H z$

$280 H z, 272 H z$

answer is C.

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Detailed Solution

$n_{1} = \frac{v}{4 l_{1}}$ and $n_{2} = \frac{v}{2 l_{2}}$ given $l_{1} = 32 c m$ ,
$l_{2} = 66 c m$ and $n_{1} - n_{2} = 8 h e a t / s$

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