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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}
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- 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}
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- 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
- 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.
See Also
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