In approaching the description of a sound wave the mathematics never gives the whole story. The subtleties of thermodynamics are difficult enough to recommend a gradual familiarization with some related problems of vibration such as arise in mechanical sound production: [motion of a spring]? [vibration of a string]? [equation of motion]? harmonic?.
Besides the the math tools that we will use again, the preceding examples help inform the beginner's physical intuition with analogies to the periodic compression domains transfer function [sound pressure]? [acoustic impedance]? [acoustic resistance]? law of gases
See [instrumental acoustics]?, [music theory]? voice production formant [speech synthesis]?