Sound pressure

From Free net encyclopedia

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 unit is pascal (symbol: Pa) and that is equal to a force F of one newton (1 N) applied over an area A of one square metre (1 m²).

The amplitude of sound pressure from a point source decreases in the free field (direct field) proportional to the inverse of the distance r from that source. That is 1/r and really not squared!
Sound pressure level is a decibel scale based on a reference sound pressure of 20 µPa (micropascals)[Air], calculated in dB as:

<math>

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

This is written "dBSPL".

Reference sound pressure p₀ = 2 × 10^-5 Pa = 20 µPa [Air]

Sound pressure p in N/m² or Pa is:

<math>

p = Zv = \frac{I}{v} = \sqrt{IZ} </math>

Z: acoustic impedance, sound impedance, or characteristic impedance; Pa·s/m

v: particle velocity; m/s

I: acoustic intensity or sound intensity; W/m²

Sound pressure p is connected to particle displacement (or particle amplitude) ξ 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 pascals.

where:

Symbol	Units	Meaning
p	Pa	sound pressure
f	Hz	frequency
ξ	m	particle displacement
c	m/s	speed of sound
v	m/s	particle velocity
ω = 2πf	rad/s	angular frequency
ρ	kg/m³	density of air
Z = c · ρ	N·s/m³	acoustic impedance
a	m/s²	particle acceleration
I	W/m²	sound intensity
E	W·s/m³	sound energy density
P_ac	W	sound power or acoustic power
A	m²	area

The distance law for the sound pressure p is inverse-proportional to the distance r of a punctual sound source. This is not like sound intensity which follows the inverse-square law.

<math>

p \propto \frac{1}{r} </math> (proportional)

<math>

\frac{p_1} {p_2} = \frac{r_2}{r_1} </math>

<math>

p_1 = p_{2} \cdot r_{2} \cdot \frac{1}{r_1} </math>

Note: The often used term "intensity of sound pressure" is nonsensical. 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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