Sound pressure, particle velocity, intensity and power
Sound pressure, particle velocity, intensity and power are different things, and mixing them up causes many errors in acoustics. They are related in a clear way, and an analogy to electricity helps.
The four quantities
| Quantity | Symbol, unit | Meaning |
|---|---|---|
| Sound pressure | p, Pa | pressure variation at a point (what a microphone measures) |
| Particle velocity | v, m/s | velocity of the air particles as they oscillate |
| Sound intensity | I, W/m² | acoustic power passing through a unit area, with direction |
| Sound power | P, W | total acoustic power emitted by a source |
Pressure is a scalar at a point. Velocity and intensity have a direction. Power is a property of the source.
A plane wave
In a plane travelling wave, pressure and velocity are in phase and linked by the characteristic impedance of air:
p = Z₀ · v, with Z₀ = ρ · c ≈ 413 Pa·s/m at 20 °C
The intensity is the product of pressure and velocity:
I = p · v = p² / Z₀
The electrical analogy
| Acoustics | Electricity |
|---|---|
| sound pressure p | voltage U |
| particle velocity v | current I |
| characteristic impedance Z₀ | resistance R |
| sound intensity I | power per area |
Ohm's law has an acoustic equivalent: p = Z₀ · v. The relation I = p²/Z₀ mirrors P = U²/R.
Levels
Each quantity has a level in decibels relative to a reference:
- L_p (sound pressure level) uses 20 µPa.
- L_I (sound intensity level) uses 1 pW/m².
- L_W (sound power level) uses 1 pW.
- Particle velocity level uses 50 nm/s.
Pressure and velocity are field quantities, so their levels use 20 · log; intensity and power are energy quantities, and their levels use 10 · log. The reference values are chosen so that L_p and L_I are nearly equal in a free field, see the sound pressure converter.
Why pressure is not power
A source radiates a certain power. The pressure it produces at a point depends on the distance, on the directivity of the source and on the room. The same loudspeaker gives a very different sound pressure level outdoors, on a hard floor and in a corner. In free space
L_p = L_W + 10 · log (Q / (4π r²))
see the sound power tool. Compare levels of different sources by their power, not by pressure at an unknown distance.
Pressure is not intensity
In a standing wave, such as a room mode, the pressure can be high where the particle velocity is zero, and the net energy flow is small. Pressure level then says little about the sound energy. Intensity probes, with two closely spaced microphones, measure the energy flow directly.
Near field
Close to a source the relationship between pressure and velocity is more complicated, and they are no longer in phase. This is the reason for proximity effect.
Draft: written by an AI assistant, awaiting technical review.
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