Acoustic energy conservation

Linear acoustic fields obey

\frac{\partial}{\partial t} (K + W) + \nabla \cdot I = 0,

where

K = \frac{1}{2} ρ_{0} ∣ u ∣^{2}, W = \frac{p ^{'2}}{2 ρ _{0} c _{0}^{2}}, I = p^{'} u .

Table of contents
- Acoustic energy density Acoustic energy conservation

Acoustic energy density ( $E$ )

For a linear acoustic perturbation of a uniform fluid,

E = \frac{1}{2} ρ_{0} ∣ u ∣^{2} + \frac{p ^{'2}}{2 ρ _{0} c _{0}^{2}}

is the sum of kinetic and compressional energy densities. Together with the acoustic energy flux

I = p^{'} u

, it satisfies

E_{t} + \nabla \cdot I = 0

.

 Ancestors (5)

 Incoming links (3)

Past exam of the mathematics course of the University of Cambridge / 2020 / ii / Paper 1 / 40B / a / Solution
Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 1 / 40C / a / Solution
Pressure-forced standing acoustic wave in a spherical annulus

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