Soundfield Quantities of a Plane Wave – The Amplitudes
German: Schallfeldgrößen einer ebenen Welle – Amplituden: http://www.sengpielaudio.com/SchallfeldgroessenEinerEbenenWelle.pdf
UdK Berlin
Sengpiel
04.2009
Schall
This particle has its minimum deflection and currently moves forward.
Thus, its sound particle velocity is strongly positive.
This particle has reached its maximum deflection and will reverse the direction of movement.
Thus, its sound particle velocity is zero.
This particle has reached its minimum deflection and moves back momentarily.
Thus, its sound particle velocity is strongly negative.
This particle has reached its maximum deflection and will reverse the direction of movement.
Thus, its sound particle velocity is zero.
Position of the air
particles at rest
Position of the air
particles in oscillating state
compression
expansion
compression
expansion
Displacement
Amplitude
Sound particle displacement / particle deflection
Particle displacement
The maximum sound pressure
velocity is at the minimum
of the particle velocity
Amplitude of
sound pressure
Sound pressure
RMS value8
Pressure gradient
between points
r1 and r2
Atmospheric pressure
101,325 Pa
The maximum particle
velocity is in the maximum
of the sound pressure
The time t or
the distance r
to the source
can be given
r = c × t (c = 343 m/s)
Amplitude of the
sound particle velocity
Sound particle velocity
RMS value
Instantaneous value
of the sound particle
velocity
Amplitude of the
pressure gradient
The pressure gradient
is always the derivative
(slope) of the particle velocity
Pressure gradient
RMS value
Instantaneous value
of the pressure gradient
From: Andreas Friesecke, "Die Audio-Enzyklopädie", K.G.Saur-Verlag, München, 2007, page 26
There are different amplitudes of sound. For a plane wave, sound pressure and particle velocity are in phase.
The simple equation pRMS = pa / √2, explains acoustic pressure amplitude pa (peak value) and sound pressure pRMS
Amplitudes of air particle displacement , sound pressure p, sound velocity v, and pressure gradient pmean all
different things as sound field quantity. Avoid the term amplitude using a sound energy quantity.
Some sound engineering publications wrongly assume that particle velocity and pressure gradient are the same.
All directional microphones exhibit the principle of the sound pressure difference  p, called pressure-gradient,
where besides the front of the microphone diaphragm more or less also the reverse side of the diaphragm is covered by sound. Therefore these sensors are called pressure-gradient receivers or pressure-gradient microphones
and have little to do with particle velocity v.
Look also at: "What is amplitude?" http://www.sengpielaudio.com/calculator-amplitude.htm
"Relationship of acoustic quantities associated with a plane progressive acoustic sound wave ":
http://www.sengpielaudio.com/RelationshipsOfAcousticQuantities.pdf
Johannes Kammann, "Sound particle velocity and pressure gradient are not the same (German)":
http://www.sengpielaudio.com/SchallschnelleIstNichtDruckgradient.pdf
Manfred Hibbing, "Sound particle velocity, pressure gradient and microphones (German)":
http://www.sengpielaudio.com/SchallschnelleDruckgradientMikrofone-HibbingMails.pdf