The linear acoustic wave equation explains the propagation of small-amplitude sound pressure waves, $p$, through a homogeneous, isotropic, and adiabatic fluid medium.

Recall that a medium is just a material through which sound travels. Sound requires a material medium because it propagates through mechanical disturbances of matter.

• homogenous fluid medium: material is uniform in space (air)
• isotropic fluid medium: material is same in every direction (still water)
• adiabatic fluid medium: No heat transfer during the compression and expansion of the sound wave

As we recall, acoustic pressure refers to the ever-so-small change in pressure ($\Delta P$) caused by a sound wave, relative to the normal pressure of the surrounding medium.

3-dimensional equation (cartesian coordinate): $\nabla^2p-\frac{1}{c^2} \space\frac{\partial^2p}{\partial t^2}=0$.

Where:

• $\nabla^2$ is the Laplace operator.
• $p(x,y,z,t)$ is acoustic pressure fluctuation (psi)
• $c$ is speed of sound in medium (ft/s)
• $t$ is time (sec)