# Sound pressure

Sound pressure p (or acoustic pressure) is the measurement in pascals of the root mean square (RMS) pressure deviation (from atmospheric pressure) caused by a sound wave passing through a fixed point. The symbol for pressure is the lower case p. (The upper case P is the symbol for power. This is often misprinted.)

The amplitude of sound pressure from a point source decreases in the free field (direct field) proportional to the inverse of the distance from that source. Sound pressure level is a decibel scale based on a reference sound pressure of 20 µPa (micropascals), calculated in dB as:

[itex]

L_p=20\, \log_{10}\left(\frac{p_1}{p_0}\right)\mathrm{dB} [itex]

This is written "dB (SPL)".

p0: Reference sound pressure of 2 × 10-5 Pa = 20 µPa

Sound pressure p in N/m2 or Pa is:

[itex]

p = Zv = \frac{J}{v} = \sqrt{JZ} [itex]

Z: acoustic impedance, sound impedance, or characteristic impedance, in Pa·s/m
v: particle velocity in m/s
J: acoustic intensity or sound intensity, in W/m2

Sound pressure p is connected to particle displacement (or particle amplitude) ξ, in m, by:

[itex]

\xi = \frac{v}{2 \pi f} = \frac{v}{\omega} = \frac{p}{Z \omega} = \frac{p}{ 2 \pi f Z} [itex]

Sound pressure p:

[itex]

p = \rho c \omega \xi = Z \omega \xi = { 2 \pi f \xi Z} = \frac{a Z}{\omega} = c \sqrt{\rho E} = \sqrt{\frac{P_{ac} Z}{A}} [itex] normally in units of N/m2 = Pa.

where:

p: sound pressure, in N/m2 = Pa
f: frequency, in Hz
ρ: density of air, in kg/m3
c: speed of sound, in m/s
v: sound velocity, in m/s
ω: angular frequency = 2π·f
ξ: particle displacement (particle amplitude), in m
Z: acoustic impedance (characteristic impedance) = c · ρ, in Pa·s/m
a: particle acceleration, in m/s2
E or w sound energy density, in J/m3
Pac sound power or acoustic power, in W
A area, in m2

Note: The often used term "intensity of sound pressure" is not correct. Use "magnitude", "strength", "amplitude", or "level" instead. "Sound intensity" is sound power per unit area, while "pressure" is a measure of force per unit area. Intensity is not equivalent to pressure.

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