[[Category:Fluid dynamics]]
'''Acoustic theory''' is the field relating to mathematical description of [[sound]] [[waves]]. It is derived from [[fluid dynamics]]. See [[acoustics]] for the [[engineering]] approach.

The propagation of sound waves in air can be modeled by an equation of motion (conservation of [[momentum]]) and an equation of continuity (conservation of [[mass]]). With some simplifications, in particular constant density, they can be given as follows:
: <math>\rho_0 \frac{\partial}{\partial t} \mathbf{v}(\mathbf{x}, t) + \nabla p(\mathbf{x}, t) = 0</math>
: <math>\frac{\partial}{\partial t} p(\mathbf{x}, t) + \rho_0 c^2 \nabla \cdot \mathbf{v}(\mathbf{x}, t) = 0</math>
where <math>p(\mathbf{x}, t)</math> is the acoustic pressure and <math>\mathbf{v}(\mathbf{x}, t)</math> is the acoustic fluid velocity vector, <math>\mathbf{x}</math> is the vector of spatial coordinates <math>x, y, z</math>, <math>t</math> is the time, <math>\rho_0</math> is the static density of air and <math>c</math> is the speed of sound in air.

==See also==
* [[Transfer function]]
* [[Sound]]
* [[Acoustic impedance]]
* [[Acoustic resistance]]
* [[Gas Laws|law of gases]]
* [[Frequency]]
* [[Fourier analysis]]
* [[Instrumental acoustics]]
* [[Music theory]]
* [[Voice production]]
* [[Formant]]
* [[Speech synthesis]]
* [[Loudspeaker acoustics]]
* [[Lumped component]] model


[[Category:Acoustics]]