Sound waves in a gas can only propagate if the gas molecules collide with each other on the time scale of the sound wave's period. Thus the highest possible frequency fmaxfmax for a sound wave in a gas is approximately equal to 1/tcolltcoll the inverse of the average collision time between molecules. Assume a gas, composed of molecules with mass mm and radius rr, is at pressure PP and temperature TT.Derive the expression for the highest sound frequency in the gas.Express your answer in terms of some or all of the variables mm, rr, PP, TT, and Boltzmann constant kk.