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Acoustic theory is a scientific field that relates to the description of sound waves. It derives from fluid dynamics. See acoustics for the engineering approach.
For sound waves of any magnitude of a disturbance in velocity, pressure, and density we have
In the case that the fluctuations in velocity, density, and pressure are small, we can approximate these as
Where v {\displaystyle \mathbf {v} } is the perturbed velocity of the fluid, p 0 {\displaystyle p_{0}} is the pressure of the fluid at rest, p ′ {\displaystyle p'} is the perturbed pressure of the system as a function of space and time, ρ 0 {\displaystyle \rho _{0}} is the density of the fluid at rest, and ρ ′ {\displaystyle \rho '} is the variance in the density of the fluid over space and time.