Extension of Previous Question: Why is the speed of sound constant in a given medium

Differences in sound waves being frequency/amplitude/wavelength. Why would all sound waves traveling in on medium move at the same speed?

Because of the way sound waves are propagated (at the molecular level) in air.

The process relies on the fact that energy is transmitted between neighbouring molecules due to their natural random thermal motion and the collisions between molecules. The speed of sound is governed by the speed of the randomly moving molecules; this speed only depends on the temperature and mass of the molecules (Sound travels faster in warmer air than cooler air.)

Whether you have a high frequency or low frequency , the thermal molecular speeds are the same, so the speed of sound is the same. See link for a bit better explanation.

For light, a completely different (and much more complex) process operates.