|Sound waves are nothing more than pressure waves that enable the air and our eardrums
to get in motion and let our eardrums and microphones vibrate. That is the sound we hear.
Do not use the expression "intensity of sound pressure". Intensity is really not sound pressure.
Compare: Sound pressure, sound pressure level, SPL, sound intensity, sound intensity level.
How much is a twice (double, half) or three times louder sound?
● For calculations with sound levels (decibels) go to:
"Damping of sound levels with distance".
A "stupid" statement: The "sound" decreases with the square of the distance.
Which sound exactly?
Of course the sound that we hear as particle displacement ξ, sound pressure p, acoustic intensity I, acoustic power Pac, particle velocity v, sound energy density w.
|p1||=||sound pressure 1 at reference distance r1 from the sound source|
|p2||=||sound pressure 2 at the other distance r2 from the sound source|
|I1||=||sound intensity 1 at reference distance r1 from the sound source|
|I2||=||sound intensity 2 at the other distance r2 from the sound source|
|The sound pressure decreases with 1/r at a distance from the sound source.
The sound intensity drops with 1/r2 at a distance from the sound source.
This is often confused and misunderstood because of the principal difference between the sound pressure as a sound field size and the sound intensity as a sound energy size is not known.
Our ear drums of our hearing and also the diaphragms of the microphones are moved effectively by the sound pressure. Sound engineers should consider this sound pressure as sound field size (quantity) more precisely; see:
Sound pressure and Sound power − Effect and Cause
Pressure as field size is never Intensity as energy size.
|Formulas to calculate the sound pressure p or the sound intensity I in dependence of the distance r to a sound source.|
|Formulas to calculate the sound level L in dB (sound pressure level or sound intensity level) in dependence of the distance r from a sound source.|
|Often we talk only of sound level. However, sound pressure as a sound field
size is not the same as sound intensity as a sound energy size.
Levels of sound pressure and levels of sound intensity decrease equally with the distance from the sound source. The sound power level has nothing to do with the distance of the sound source. Compare: A 100 watt light bulb has in 1 m and in 10 m distance really always the same 100 watts, which is emmited from the bulb all the time.
Sound pressure level und sound intensity level
|To use the calculator, simply enter a value.
The calculator works in both directions of the ↔ sign.
Threshold of hearing = Reference sound pressure p0 = 20 μPa = 2 · 10−5 Pa ≡ 0 dB Pa = N/m2
Threshold of hearing = Reference sound intensity I0 = 1 pW/m2 = 10−12 W/m2 ≡ 0 dB
|Pressure, velocity, and intensity of the sound field near to and
distant from a spherical radiator of the zeroth order
For a spherical wave:
|A spherical wavefrontis formed under the assumption of idealized conditions, such
as a spherical radiator of zero order (ie, a "breathing" sphere) as a source for
radiation in a homogeneous isotropic medium, usually air.
For the dropping of sound pressure p and of particle velocity v we get in the far field:
(r is the distance from the measurement point to the sound source).
All sound field sizes decrease in the far field after the 6-dB-distance law 1/r.
Exception: The sound velocity goes with 1/r² in the near field . That is, the size values
are halved by distance doubling. The sound intensity increases as the sound energy
size is proportional to the square of the distance from the sound source
decreases permanent from the sound source. Since the radiated sound power from
the sound source as sound intensity is distributed on a growing area with the
distance, the sound intensity falls off in the same proportion as the area grows larger.
envelope to the spherical sound source, that is, power is independent of the
distance r to the sound source.
Sound power Pak in W, sound intensity I in W/m², distance from measuring point r in m,
and area A in m².
|Ear people, like sound engineers and sound designers are mainly
interested in sound field sizes, and therefore consider the sound pressure
drop at distance doubling.
Acousticians and noise fighters are mainly interested in sound energy sizes, and therefore consider more the active intensity increase at distance doubling.
All persons consider together the same line! Is this not beautiful? Nevertheless, the drop in sound pressure goes with 1/r and the decrease in sound intensity with 1/r2. This should be understood all right.
If you are a sound engineer to review the sound quality by ear, then think of the sound waves, which move the eardrums effectively by the sound pressure as sound field size. There is also the advice: Try to avoid to use the words sound power and sound intensity as sound energy sizes.
We do not hear the air pressure changes as such, but the sound
pressure at each ear, which is superimposed to the air pressure.
|Some more useful links:
Damping of sound level with distance
Sound pressure p and the inverse distance law 1/r
Sound intensity I and the inverse square law 1/r²
Conversion of sound units (levels)
Subjectively perceived loudness and objectively measured sound pressure
Sound sizes, their Levels and References - Calculations, and Formulas
Relationship of acoustic sizes
Comparative representation of sound field sizes and sound energy sizes
Sound pressure and Sound power − Effect and Cause
Table of Sound Levels (dB Scale)
The Formula Wheel - Formulas of Acoustics (Audio)
Acoustic equivalent for ohm's law - ohm's law as equivalent in the acoustics
In audio, electronics and acoustics use only the word "damping" and not the wrong word "dampening".
1. a decreasing of the amplitude of an electrical or mechanical wave.
2. an energy-absorbing mechanism or resistance circuit causing this decrease.
3. a reduction in the amplitude of an oscillation or vibration as a result of energy being dissipated as heat.
1. To make damp.
2. To deaden, restrain, or depress.
3. To soundproof.
Notice: Damping is energy dissipation and dampening is making something wet.