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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 $51^{0} C$ or $16^{0} C .$ The frequency of the tuning fork is

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128 Hz

256 Hz

98 Hz

105 Hz

answer is C.

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Detailed Solution

We now $n α \sqrt{T}$

$\frac{n_{1}}{n_{2}} = \sqrt{\frac{T_{1}}{T_{2}}}$

$\frac{n + 3}{n-3} = \sqrt{\frac{51 + 273}{16 + 273}}$

$\frac{n + 3}{n-3} = \sqrt{\frac{324}{289}}$

$\frac{n + 3}{n-3} = \frac{18}{17}$

By solving we get n= 105 Hz

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