**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.

and the momentum balance and mass balance are expressed as

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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.

Propagation of sound waves in a fluid (such as water) can be modeled by an equation of continuity (conservation of mass) and an equation of motion (conservation of momentum) . With some simplifications, in particular constant density, they can be given as follows:

where $p(\mathbf {x} ,t)$ is the acoustic pressure and $\mathbf {u} (\mathbf {x} ,t)$ is the flow velocity vector, $\mathbf {x}$ is the vector of spatial coordinates $x,y,z$, $t$ is the time, $\rho _{0}$ is the static mass density of the medium and $\kappa$ is the bulk modulus of the medium. The bulk modulus can be expressed in terms of the density and the speed of sound in the medium ($c_{0}$) as

If the flow velocity field is irrotational, $\nabla \times \mathbf {u} =\mathbf {0}$, then the acoustic wave equation is a combination of these two sets of balance equations and can be expressed as

where we have used the vector Laplacian, $\nabla ^{2}\mathbf {u} =\nabla (\nabla \cdot \mathbf {u} )-\nabla \times (\nabla \times \mathbf {u} )$ . The acoustic wave equation (and the mass and momentum balance equations) are often expressed in terms of a scalar potential $\varphi$ where $\mathbf {u} =\nabla \varphi$. In that case the acoustic wave equation is written as

and the momentum balance and mass balance are expressed as

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