Introduction

Now we are going to analyze the wave motion in the air, this is the most important type of wave motion studied in the science of acoustics. Sound waves differ from the waves we have analyzed before in several respects. Sound waves are waves in three dimensions and as such can be more complicated in behavior than waves in two dimensions or in one. Sound waves also differ from waves on a string or on membrane by being longitudinal waves.

Standard vibrations that we have analyzed are in form of transverse waves. These are the waves in which material that is transmitting the wave moves in a direction which is perpendicular to the propagation of the wave. The transverse wave is shown in next figure.

Figure 1 - Transverse Wave

If we analyze the vibration of the simple string we can conclude that the portions of the string move in direction at right angles to the equilibrium shape of the string, whereas the wave travels along the string. Molecules of air in presence of sound move in the same direction as the propagation of the wave. This type of motion is called longitudinal wave motion. In this type of wave motion there are no oscillations that are perpendicular to the wave propagation. 

Figure 2 - Longitudinal wave

Since the sound waves are more complicated than standard oscillation because they are waves in three dimensions we shall first analyze the plane sound waves. These waves have the same directions of propagation everywhere in space and amplitudes of plain waves are in planes which are perpendicular to the direction of propagations. These plain waves are similar to the parallel waves on a membrane. Waves that you here form the distant source can be approximated as plain waves.

In general properties of acoustic wave motion depend on the ratios between the amplitude and frequency of the acoustic motion and the molecular mean free path. In order to develop the wave equation that describes acoustic wave motion in the fluid we will need to be familiar with thermodynamic properties of the fluid and fluid dynamics. Of course we will start by analyzing the simplest case and then start building our knowledge on that. Simplest case would be the analysis of the idealized fluid which is uniform and continuous in its properties, at rest in thermodynamic equilibrium, except for the motion caused by the sound waves themselves, and with this acoustic motion small enough in magnitude so that many nonlinear effects can be neglected.