Use the formula `v = sqrt(( gamma p )/(rho ))` to explain why the speed of sound in air increases with temperature.

Explanation

Effect of temperature on velocity of sound in air `//` gas `:`
Consider PV = RT
At constant pressure `( P m )/( rho ) = RT `
i.e., `( p )/( rho ) = ( R )/ ( m ) T`
Hence in the formula `v = sqrt(( PV)/( rho ))`, 'v' may be written as `v = sqrt( gamma ((R )/( m )) T)`
or `v = sqrt(( gamma r T )/( nM))` where n = number of moles, M = Molar mass in 'g'
`gamma-` ratio of specific heats of a gas, T = absolute temperature
i.e., `v prop sqrt( T ) `.
so that `(v_(1))/( v_(2)) = sqrt((T_(1))/(T_(2))) ` where `T = 273 + t, t - ` is in `""^(@)C` .
Hence the velocity of sound in air `//` gas is directly proportional to square root of its absolute temeprature. i.e., as temperature increases, velocity of sound also increases.