Particle Velocity and adiabatic/isothermal propagation

[michaelpos]

This is a question that has been bugging me for a little while. If sound propagation in air changes from an adiabatic to an isothermal process (for example via the use of fiberglass or other heat conducting material), the wave velocity is lowered due to the reduction in the bulk modulus of air. My question is: is the particle velocity also effected by the change from adiabatic to isothermal process, or is the particle velocity independent of this?

 

[John Park]

If the gas is in equilibrium, the particle speeds depend only on the temperature; so in a isothermal process they should be unchanged. If the propagation is adiabatic, the pressure changes of the sound waves will cause temperature changes in the gas, and as a result the mean speeds will oscillate--provided that the frequency of the sound is low enough for thermal equilibrium to be maintained. (I don't know how low is "low enough". )