Two closed pipes have the same fundamental frequency. One is filled with oxygen and the other with hydrogen…
Two closed pipes have the same fundamental frequency. One is filled with oxygen and the other with hydrogen at the same temperature. Ratio of their lengths respectively is
$1:4$
$4:1$
$1:2$
$2:1$
Solution
The fundamental frequency,
$\begin{aligned}
& f=\frac{v}{4 l}=\frac{1}{4 e} \sqrt{\frac{\gamma R T}{M_0}} \\
& \ell \propto \frac{1}{\sqrt{M}} \Rightarrow \frac{\ell_1}{\ell_2}=\sqrt{\frac{M_1}{M_2}}=\sqrt{\frac{2}{32}}=\frac{1}{4}
\end{aligned}$
So, $\ell_1: \ell_2=1: 4$