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Linear Acoustic Equation

Notes:

To start, let me show where the linear acoustic equation comes from. On the left is the conservation of mass equation, which states for a fixed volume, the amount of material in has to equal the amount of material out.
The second is Euler's equation, which describes how a small piece of the fluid will react to external forces.
Both of these equations are linearized by setting the variable to a constant plus a first order perturbation.
The curl of Euler's equation yields the scalar velocity potential, which is commonly used.