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Acoustic theory

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:

\rho_0 \frac{\partial}{\partial t} \mathbf{v}(\mathbf{x}, t) + \nabla p(\mathbf{x}, t) = 0
\frac{\partial}{\partial t} p(\mathbf{x}, t) + \rho_0 c^2 \nabla \cdot \mathbf{v}(\mathbf{x}, t) = 0

where p(\mathbf{x}, t) is the acoustic pressure and \mathbf{v}(\mathbf{x}, t) is the acoustic fluid velocity vector, \mathbf{x} is the vector of spatial coordinates x,y,z, t is the time, ρ0 is the static density of air and c is the speed of sound in air.

See also

  • Transfer function
  • Sound
  • Acoustic impedance
  • Acoustic resistance
  • law of gases
  • Frequency
  • Fourier analysis
  • Instrumental acoustics
  • Music theory
  • Voice production
  • Formant
  • Speech synthesis
  • Loudspeaker acoustics
  • Lumped component model
This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Acoustic_theory". A list of authors is available in Wikipedia.
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