Sound pressure
Sound quantities 

The sound pressure or alternating sound pressure , symbol p ("pressure"), is the most important sound field quantity in sound engineering and acoustics . The SI unit of sound pressure, like pressure, is the pascal with the unit symbol Pa. The sound pressure level in dB can be calculated from the rms value of the sound pressure .
definition
Sound pressure refers to the pressure fluctuations in a compressible sound transmission medium (usually air ) that occur when sound propagates . These pressure fluctuations are converted by the eardrum as a sensor into movements for hearing sensation.
The sound pressure p is the alternating pressure (an alternating quantity ) which is superimposed on the static pressure p _{0} ( air pressure ) of the surrounding medium. Here is the alternating sound pressure
with the area A acting force F per surface area of A .
The following applies to the entire pressure p _{tot} :
The sound pressure p (alternating sound pressure ) is usually many orders of magnitude smaller than the static air pressure. Since a pressure cannot be linked to any direction specification, it is a scalar quantity. From a mathematical point of view, the sound pressure as a function of the coordinates in threedimensional space is therefore a scalar field .
Furthermore, in the case of sinusoidal signals, it is specified as an effective value
common. The sound pressure amplitude, on the other hand, is the peak value of the sound pressure.
If the sound is a tone , i.e. a harmonic oscillation (often also referred to as a " sine oscillation") with only one frequency , then the following applies to the time dependence of the sound pressure:
where the sound pressure amplitude and ω is the angular frequency .
Distance dependency
The effective value of the sound pressure in the free field is inversely proportional to the distance r from a (point) sound source (1 / r law, distance law ):
= Sound pressure at a distance = sound pressure at a distance
(Note: The quadratic sound energy quantities , such as the sound intensity , decrease with 1 / r ^{2} over the distance in the case of point sources of sound .) As you can see here, in addition to the indication of the measured sound pressure, it is essential to assess the strength of a sound source the specification of the position of the measuring point as distance r from the sound source is necessary.
In reverberant surroundings, the 1 / r law only applies to a limited extent:
 In the direct field of the sound source, i.e. outdoors and where the direct sound D outweighs the room sound R, the 1 / r law applies .
 Outside the immediate direct field, where the reflections have an impact on the total sound pressure, the 1 / r law only applies to a limited extent.
 Outside the reverberation radius r _{H} , that is the distance from the sound source at which the direct sound D is just as strong as the room sound R, the sound pressure remains essentially constant as the distance from the sound source increases, as it is mainly dependent on the reflections of the Walls is determined.
Connection with other acoustic quantities
In a plane wave , the sound pressure is linked to the acoustic parameters sound impedance , sound power , sound velocity and sound intensity as follows:
 .
Where:
symbol  units  meaning 

Pa  Sound pressure  
Hz  frequency  
m  Sound deflection  
m / s  Speed of sound  
m / s  Speed of sound  
1 / s  Angular frequency  
kg / m ^{3}  Air density (density of the medium)  
N · s / m ^{3}  Characteristic acoustic impedance, acoustic field impedance  
m / s ^{2}  Sound acceleration  
W / m ^{2}  Sound intensity  
W s / m ^{3}  Sound energy density  
W.  Sound power  
m ^{2}  Transmitted surface 
Table: Sound pressure and sound pressure level of various sound sources
Sound pressure in air
 For comparison
 static air pressure at sea level: approx. 100 kPa
Sound source and situation (distance) 
Sound pressure (effective value) (in Pascal)

Sound pressure level L _{p} dB re 20 µPa 

M1 Garand rifle (1 m)  5000  168 
Jet plane (30 m)  600  150 
Pain threshold  100  134 
Hearing damage from shortterm exposure  20th  from 120 
Jet plane (100 m)  6 ... 200  110 ... 140 
Jackhammer (1 m); discotheque  2  100 
Longterm exposure to hearing damage more than 8 hours a day 
0.6  from 90 
Main road (10 m)  0.2 ... 0.6  80 ... 90 
Car (10 m)  0.02 ... 0.2  60 ... 80 
TV at room volume (1 m)  0.02  approx. 60 
normal conversation (1 m)  2 ... 6 · 10 ^{−3}  40 ... 50 
very quiet room  2 ... 6 · 10 ^{−4}  20 ... 30 
Rustling leaves, calm breathing  6 · 10 ^{−5}  10 
Hearing threshold at 1 kHz  2 · 10 ^{−5}  0 
Sound pressure in water
 For comparison
 static pressure at sea level on the water surface: approx. 100 kPa
 in 100 m water depth: approx. 1100 kPa
 in 5 km water depth: approx. 51 100 kPa
Sound source and situation (distance) 
Sound pressure (in pascal) 
Sound pressure level L _{p} dB re 1 µPa 

military sonar (1 m)  10 ^{6}  240 
Diver's hearing threshold at 1 kHz  2.2 · 10 ^{−3}  67 
literature
 Hans Breuer: dtvAtlas Physik , Volume 1. Mechanics, acoustics, thermodynamics, optics . dtv, Munich 1996, ISBN 342303226X
 Heinrich Kuttruff: Acoustics . Hirzel, Stuttgart 2004, ISBN 3777612448
 Gerhard Müller, Michael Möser: Paperback of technical acoustics . 3. revised Edition. Springer, Berlin 2003, ISBN 3540412425
 Ivar Veit: Technical acoustics . VogelVerlag, Würzburg 2005, ISBN 3834330132
Web links
 Basics and terms in terms of sound technology  sound pressure
 Acoustic waves and fields (PDF; 1.0 MB)
 Sound quantities, their levels and the reference value  conversions, calculations and formulas