Sound pressure

Sound measurements
Characteristic	Symbols
Sound pressure	p, SPL
Particle velocity	v, SVL
Particle displacement	δ
Sound intensity	I, SIL
Sound power	P, SWL
Sound energy	W
Sound energy density	w
Sound exposure	E, SEL
Acoustic impedance	Z
Speed of sound	c
Audio frequency	AF
Transmission loss	TL

Sound pressure or acoustic pressure is the local pressure deviation from the ambient (average, or equilibrium) atmospheric pressure, caused by a sound wave. In air, sound pressure can be measured using a microphone, and in water with a hydrophone. The SI unit of sound pressure is the pascal (Pa).

A sound wave in a transmission medium causes a deviation (sound pressure, a dynamic pressure) in the local ambient pressure, a static pressure.
Sound pressure, denoted p, is defined by

where

In a sound wave, the complementary variable to sound pressure is the particle velocity. Together they determine the sound intensity of the wave.
Sound intensity, denoted I and measured in W·m⁻² in SI units, is defined by

where

Acoustic impedance, denoted Z and measured in Pa·m⁻³·s in SI units, is defined by

where

Specific acoustic impedance, denoted z and measured in Pa·m⁻¹·s in SI units, is defined by

where

The particle displacement of a progressive sine wave is given by

where

It follows that the particle velocity and the sound pressure along the direction of propagation of the sound wave x are given by

where

Taking the Laplace transforms of v and p with respect to time yields

Since ${\displaystyle \varphi _{v,0}=\varphi _{p,0}}$, the amplitude of the specific acoustic impedance is given by

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