Sound pressure
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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 (micropascals), calculated in dB as:
- <math>
L_p=20\, \log_{10}\left(\frac{p_1}{p_0}\right)\mathrm{dB} <math>
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:
- <math>
p = Zv = \frac{J}{v} = \sqrt{JZ} <math>
- 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:
- <math>
\xi = \frac{v}{2 \pi f} = \frac{v}{\omega} = \frac{p}{Z \omega} = \frac{p}{ 2 \pi f Z} <math>
Sound pressure p:
- <math>
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}} <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 Pa·s/m
- a: particle acceleration, in m/s2
- E or w sound energy density, in J/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.
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)de:Schalldruck
it:Pressione acustica nl:Geluidsdruk pl:Ciśnienie akustyczne