Question

Under similar conditions of temperature and pres-
sure, two gases (x and y) of equal masses are taken
such that x and y occupy volumes of 2 litre and 50 litre,
respectively. When sound waves are passed through
both the gases, in which gas does sound travel with a greater velocity? ​

Answer 1

$\sf \Large Solution!!$

$\sf \large Given,$

$\sf \to V_{1}=2\;litre$

$\sf \to m_{1}=x$

$\sf \to V_{2}=50\;litre$

$\sf \to m_{2}=x$

$\sf \large We\;know\;that\;$

$\sf \boxed{\bigstar V\propto \frac{1}{\sqrt{d}}}$

$\sf \large So,$

$\sf \to d_{1}=\frac{m_{1}}{V_{1}}$

$\sf \to d_{1}=\frac{x}{2\;litre}$

$\sf \to d_{2}=\frac{m_{2}}{V_{2}}$

$\sf \to d_{2}=\frac{x}{50\;litre}$

$\sf \boxed{d_{1}\;will\;be\;more\;than\;d_{2}\;because\;the\;velocity\;is\;more\;in\;d_{2}\;than\;in\;d_{1}.}$

$\sf \to d_{1}>d_{2}\quad (More\;the\;density,\;less\;the\;velocity)$

$\sf \to Velocity\;of\;gas\;x\;is\;less\;as\;compared\;to\;gas\;y$

$\sf \boxed{\bigstar Sound\;will\;travel\;in\;gas\;y\;with\;greater\;velocity!!}$