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Concept
Sound pressure
Summary
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
ptotal is the total pressure,
pstat is the static pressure.
Sound intensity
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
p is the sound pressure,
v is the particle velocity.
Acoustic impedance
Acoustic impedance, denoted Z and measured in Pa·m−3·s in SI units, is defined by
where
is the Laplace transform of sound pressure,
is the Laplace transform of sound volume flow rate.
Specific acoustic impedance, denoted z and measured in Pa·m−1·s in SI units, is defined by
where
is the Laplace transform of sound pressure,
is the Laplace transform of particle velocity.
Particle displacement
The particle displacement of a progressive sine wave is given by
where
is the amplitude of the particle displacement,
is the phase shift of the particle displacement,
k is the angular wavevector,
ω is the angular frequency.
It follows that the particle velocity and the sound pressure along the direction of propagation of the sound wave x are given by
where
vm is the amplitude of the particle velocity,
is the phase shift of the particle velocity,
pm is the amplitude of the acoustic pressure,
is the phase shift of the acoustic pressure.
Official source
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