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• # Soundwave energy

Posted by on May 6, 2023 at 6:01 PM

Soundwave energy is kinetic, and potential energy through a transmission medium (such as a gas, liquid, or solid) due to a sound propagated a wave of pressure (a particular form of a mechanical wave).

The sound is transmitted through gases, plasma, and liquids as longitudinal waves also called compression waves. It requires a medium to propagate. Through solids, however, it can be transmitted as both longitudinal waves and transverse waves. Longitudinal sound waves are waves of alternating pressure deviations from the equilibrium pressure, causing local regions of compression and rarefaction, while transverse waves (in solids) are waves of alternating shear stress at a right angle to the direction of propagation.

Consequently, the sound energy in a volume of interest is defined as the sum of the potential and kinetic energy densities integrated over that volume:

$W = W_\mathrm{potential} + W_\mathrm{kinetic} = \int_V \frac{p^2}{2 \rho_0 c^2}\, \mathrm{d}V + \int_V \frac{\rho v^2}{2}\, \mathrm{d}V$

where:

• $$V$$ is the volume of interest;
• $$p$$ is the sound pressure;
• $$v$$ is the particle velocity;
• $$\rho_0$$ is the density of the medium without sound present;
• $$\rho$$ is the local density of the medium;
• $$c$$ is the speed of sound.
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