How does chemical relaxation change the speed of sound in a gas?

Chemical relaxation influences the speed of sound in a gas by causing dispersion, which refers to frequency-dependent changes in sound velocity.1

When a sound wave propagates through a gas, it creates alternating fluctuations in pressure and temperature. If the frequency of these oscillations is low, the chemical equilibrium (such as the dissociation of nitrogen tetroxide into nitrogen dioxide) can adjust instantaneously to follow the pressure and temperature changes.1

However, at intermediate frequencies, the chemical reaction cannot keep pace with the rapid fluctuations, causing the readjustment of the chemical equilibrium to lag behind the pressure variations. This lag results in the dispersion of the sound velocity. By measuring these changes in velocity, as well as the associated absorption of sound, scientists can determine the relaxation time of the chemical system, which provides insight into the reactivities and mechanisms of the chemical species involved.1