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 �Pa (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 �Pa

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:

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

P_ac 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.

Sound measurements

Sound power
Sound power level (SWL)
Sound pressure
Sound pressure level (SPL)
Sound intensity
Sound intensity level (SIL)
Particle velocity
Particle velocity level (sometimes called Sound velocity level) (SVL)
Sound energy flux
Acoustic impedance
Speed of sound

Sound pressure

Sound measurements

External links

See also: Sound pressure, Acoustic impedance, Acoustic intensity, Acoustic power, Amplitude, Angular frequency, Area, Atmospheric pressure, Characteristic impedance