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Sound Pressure
Find Sound pressure
Sound pressure Info


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:

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

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:

p = Zv = \frac{J}{v} = \sqrt{JZ}
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:

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

Sound pressure p:

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}}

normally in units of N/m2 = Pa.

where:

Symbol Units Meaning
p pascals sound pressure
f hertz frequency
ρ kg/m3 density of air
c m/s speed of sound
v m/s particle velocity
ω = 2 · π · f radians/s angular frequency
ξ meters Particle displacement
Z = c · ρ N·s/m³ acoustic impedance
a m/s² Particle acceleration
J W/m² sound intensity
E W·s/mm³ sound energy density
Pac watts sound power or acoustic power
A m² Area


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.

Sound measurements

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