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:

$p = Z \cdot v = \frac{J}{v} = \sqrt{J \cdot Z}$

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:

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

Sound pressure p:

$p = \rho \cdot c \cdot \omega \cdot \xi = Z \cdot \omega \cdot \xi = {\xi \cdot Z \cdot 2 \cdot \pi \cdot f} = \frac{a \cdot Z}{\omega} = c \cdot \sqrt{\rho \cdot E} = \sqrt{\frac{P_{ac} \cdot Z}{A}}$

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.

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Categories: Sound | Acoustics

Last updated: 10-16-2005 21:30:45

Sound pressure - Your Art History Reference Guide!

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