In the case of a traveling sound wave in air, the compression and rarefaction waves both propagate at the same speed. In a longitudinal sound wave, such as a sound wave in air, particles in the medium oscillate back and forth parallel to the direction of wave propagation.
Compression waves correspond to the regions of high pressure, where air particles are compressed and closer together than in their equilibrium state. Rarefaction waves, on the other hand, correspond to the regions of low pressure, where air particles are relatively more spread out compared to their equilibrium state.
As the sound wave propagates, both the compression and rarefaction waves travel at the same speed through the air medium. The speed of sound in a particular medium depends on the properties of the medium, such as its density and elasticity. In dry air at room temperature, the speed of sound is approximately 343 meters per second (or around 1,125 feet per second).
Therefore, whether it's the compression wave or the rarefaction wave, both components of the sound wave propagate through the air medium at the same speed, contributing to the overall movement of the sound wave.