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 (micropascal), calculated in dB as:

<math>

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

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

Sound pressure p in N/m² or Pa is:

<math>

p = Z \cdot v = \frac{J}{v} = \sqrt{J \cdot Z} <math>

Z: acoustic impedance, sound impedance, or characteristic impedance, in N·s/m³

v: acoustic velocity, sound velocity, or 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:

<math>

\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} <math>

Sound pressure p:

<math>

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}} <math> 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 N·s/m³

a: particle acceleration, in m/s²

E or w sound energy density, in W·s/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.

See Also

• Sound pressure level
• Sound intensity

External links

• Ohm's law of the acoustics - calculations (http://www.sengpielaudio.com/calculator-ak-ohm.htm)
• Conversion: sound pressure to sound pressure level (http://www.sengpielaudio.com/calculator-soundlevel.htm)

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