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(C) The frequency of an air column in a resonance tube is proportional to the speed of sound,which is proportional to the square root of the absolute

Vedclass · Accepted Answer

$105$

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(C) The frequency of an air column in a resonance tube is proportional to the speed of sound,which is proportional to the square root of the absolute temperature $(v \propto \sqrt{T})$.Let $n$ be the frequency of the tuning fork.At $T_1 = 273 + 51 = 324 \ K$,the frequency of the air column is $n_1 = n + 3$.At $T_2 = 273 + 16 = 289 \ K$,the frequency of the air column is $n_2 = n - 3$.Using the relation $\frac{n_1}{n_2} = \sqrt{\frac{T_1}{T_2}}$,we get:$\frac{n+3}{n-3} = \sqrt{\frac{324}{289}} = \frac{18}{17}$.Cross-multiplying gives: $17(n + 3) = 18(n - 3)$.$17n + 51 = 18n - 54$.$n = 51 + 54 = 105 \ Hz$.

When the air column of a resonance tube is vibrated together with a tuning fork,$3$ beats are heard per second,either the temperature of the air column is $51^{\circ} C$ or $16^{\circ} C$. The frequency of the tuning fork is (in $Hz$)

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