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PART - 2 CH - 14 Waves — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsPART - 2 CH - 14 Waves2 Marks
Question
If carbon dioxide $\left( CO _2\right)$ gas is filled in the resonance tube appartus insted of air, then what will be the difference in the length of the resonance tube if the tube tunning frok is used?
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Answer

If $CO _2$ gas is filled in the resonant tube appartus instead of air, then the length of the column of resonant $CO _2$ will be less air column. It will be following :
Fundamental frequency $n =\frac{ v }{2 l}$
$n =\frac{ v }{2 l} \quad \Rightarrow l=\frac{ v }{2 n }$
$\begin{array}{ll}\Rightarrow & l \propto v \quad(\prime n =\text { constant }) \\ \text { But } & v =\sqrt{\frac{\gamma P }{ d }} \Rightarrow v \propto \frac{1}{\sqrt{d}}\end{array}$
Due to heavily weight of $CO _2$ sound velocity in air is less.
Therefore, the length of resonant air column is less in $CO _2$ will be.

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