An open organ pipe of length L is filled with an equimolar mixture of a monatomic gas and a rigid diatomic gas at a constant temperature. If the fundamental frequency of the pipe is f , the root mean square speed of the gas molecules in the mixture is

Step-by-step solution

For an equimolar mixture, the mole fraction of each gas is 1 2 . The molar heat capacity at constant volume for the mixture is: C_ v,mix = 1 2 ( 3 2 R ) + 1 2 ( 5 2 R ) = 2R The molar heat capacity at constant pressure for the mixture is: C_ p,mix = C_ v,mix + R = 3R The adiabatic index of the mixture is: _ mix = C_ p,mix C_ v,mix = 3 2 = 1.5 The fundamental frequency of an open organ pipe is given by f = v_s 2L , where v_s is the speed of sound in the gas. v_s = 2Lf The root mean square speed v_ rms is related to