Formula wheel acoustics audio sound pressure pie calculation sound fundamentals particle velocity units acoustic impedance Z audio engineering formulas sound intensity specific acoustic impedance sound recording - sengpielaudio
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The Formula WheelFormulas of Acoustics (Audio) 
  for sound pressure p, particle velocity v, specific acoustic impedance of air Z, sound intensity I or J
Magic circle − Formulas for calculating any combination of acoustical units – audio engineering formulas
Principles of Acoustic Law and Sound
Equations in Analogy (Relationship) to the

Ohm's Law. 
Formulary and Audio Equations
 Formula Wheel  Important Formulas
of Acoustics + Audio   of Sound + Noise
Acoustical formulas as circle diagram (pie chart)
Formula wheel acoustics
In acoustics and audio engineering sound pressure, air particle velocity, and acoustic impedance
sound field quantities. The sound intensity is a sound energy quantities.
Sound pressure p = Z × v = J / v = √(J × Z) in Pa             Particle velocity v = p / Z = J / p = √(J / Z) in m/s
Acoustic impedance Z = p / v = J / v2 = p2 / J in N·s/m3      Sound intensity J = p × v = Z × v2 = p2 / Z in W/m2
Specific acoustic impedance Z0 = ρ × c = p / v in N·s/m3.
As characteristic impedance of air we use the round value
Z0 = 400 Ns/m. Then the "sound level" as a decibel value is exactly the same of the sound pressure level and the sound intensity level.
Conversion: Sound pressure to Sound intensity and vice versa
Specific acoustic impedance of air at 20C is Z0 = 413 N·s/m.
Density of air ρ in kg/m3
Speed of sound c = λ × f in m/s
Sound power (acoustical power) Pac = J × A = p × v × A in W
Area A = 4π × r2 in m2
Sound intensity J = Pac / A =  Pac/ 4π × r2 in W/m2
Particle velocity v = (E / ρ) in m/s     E  =Sound energy density
Particle displacement ξ = p / (ω × ρ0 × c) in m (RMS)
Angular frequency ω = 2π × f  
Amplitude of sound waves (sound amplitudes) and audio signals
Acoustics, sound, and vibrations − Acoustic equivalent for ohm's law 
See also: The formula wheel of electrical engineering
Electric current, electric power, electricity − Formulas and calculations

Acoustics and vibrations − Acoustic equivalent for ohm's law
The Relation of soundsizes − Their levels and references − conversions
Relationship of acoustic sizes (quantities)
Soundfield Quantities of a Plane Wave − Amplitudes

Effect and Cause - Sound pressure and Sound power
Sound Sound Sound - sound pressure intensity acoustic impedance

Decrease of the soundfield
Pressure, velocity, and intensity of the sound field near to and
distant from a spherical radiator of the zeroth order

  Inverse distance law p Tilde 1/r for sound pressure                 Inverse square law J Tilde 1/r² for acoustic intensity
Inverse Distance Law        Inverse Square Law

Sound pressure, Sound intensity and their Levels

The following calculator shows the often desired direct conversion of sound pressure to sound intensity and vice versa with the specific acoustic impedance of air
Z0 = 400 N·s/m3.
To use the calculator, simply enter a value.
The calculator works in both directions of the

Sound field quantity   Sound energy quantity
Sound pressure p (air)
Pa (pascal)
 ↔  Sound intensity I (air)
Formel   Formel
Reference sound pressure p0 = 20 μPa = 2 × 10−5 Pa      Reference intensity I0 = 1 pW/m2 = 10−12 W/m2
Specific acoustic impedance of air Z0 = 400 N·s/m3   Sound pressure p = √ (I × Z0)   Intensity I = p2 / Z0
Sound field quantity   Sound energy quantity
Sound pressure level Lp (air)
dB (decibel)
 ↔  Sound intensity level LI (air)
dB (decibel)
Schalldruckpegel   Schallintensitaetspegel
Reference sound pressure p0 = 20 μPa = 2 × 10−5 Pa      Reference intensity I0 = 1 pW/m2 = 10−12 W/m2
The same "sound level" in dB at Specific acoustic impedance of air Z0 = 400 N·s/m3
While the distance dependent sound pressure level in the air
is matched with the sound intensity level when a reference sound characteristic impedance
Z0 =  400 N·s/m³ is chosen, this is not the case with the distance independent sound power level.

Sound pressure and
Sound pressure level 

      Sound as pressure dB scale
Note: The radiated sound power (sound intensity) is the
cause and the
sound pressure is the effect,
where the sound engineer is particularly interested in the effect.
The effect of temperature and sound pressure:
Sound pressure and Sound power – Effect and Cause
Acousticians and sound protectors ("noise fighters") need the sound intensity (acoustic intensity) – but sound engineers and sound designers ("ear people") don't need that sound energy quantity. The eardrums (tympanic membranes) of our hearing and the diaphragms of the microphones are effectively moved by the sound pressure or the sound pressure level. See also: SPL meter.
If you are a technician checking the sound quality by listening with your hearing, think of the sound waves that move your eardrums by the effect of the sound pressure as sound field size. That is why there is the advice:
In sound recording try to avoid the use of sound power and sound intensity as sound energy sizes.

How many decibels (dB) is the sound energy W = I×t×A in J = W×s?
This question is asked quite rare. For calculations we use more the following sound energy sizes: Sound energy density w or E = I / c in J/m3, sound intensity I = Pac / A in W/m2, and sound power Pac in W = J/s and their corresponding levels.

Sound waves move our eardrums (tympanic membranes).
But which sound quantity produces this effect?

Perception of sound

Sound pressure and Sound power – Effect and Cause
Sound power is the cause - but sound pressure produces the audible effect.

How to measure sound pressure?

SPL Meter
The question: "Is noise level really the sound intensity level?" will be differently answered by musicians and sound engineers as "ear people" than by acousticians. We measure the sound of music with a sound level meter
(SPL meter) and our eardrums are effectively moved by the sound pressure or its level. A sound engineer thinks that a sound level has mainly to do with the sound pressure deviations.
Acousticians as "sound fighters" have a slightly different point of view.
They mainly like to calculate the energy (power) of the sound.
Neither the sound power Pac nor the sound power level LW decreases when the distance is in doubled. Why is this so?
The sound power level quantifies the totally radiated sound energy from an object.
The noise power level is independent of the distance to the object, the surrounding area and other influences.

Notice: The psychoacoustic subjective sensations of loudness do not
belong to those predictable and measurable sound quantities; see:

Correlation between volume level in phone and loudness in sone
We feel and judge sound events as:
− exposure duration
− spectral composition
− temporal structure
− sound level
− information content
− subjective mental attitude
In sound engineering there is no Power matching or Impedance matching.
In audio we use only
Voltage bridging or high Impedance bridging.
Sound pressure p = v × Z0      (Acoustic ohm's law)
Sound pressure = particle velocity × acoustic impedance
Please enter two values, the third value will be calculated.
Sound pressure p  Pa Acoustic ohms law
Particle velocity v  m/s
 Acoustic impedance Z0  N·s/m³ 
p = v × Z0                    v = p ⁄ Z0                    Z0 = p ⁄ v
Specific acoustic impedance of air is Z = 413 N·s/m³ at 20°C.

Sound intensity J = p × v      (Acoustic power law)
Sound intensity = sound pressure × particle velocity
Please enter two values, the third value will be calculated.
                Sound intensity J  W/m²  Acoustic power law
Sound pressure p  Pa
Particle velocity v  m/s
J = p × v                    p = J ⁄ v                    v = J ⁄ p
Acoustic impedance Z0 = ρ × c
Acoustic impedance of air = density of air × speed of sound in air
Please enter two values, the third value will be calculated.
 Acoustic impedance Z0  N·s/m³  Acoustic Impedance
Density of air ρ  kg/m³
Speed of sound c  m/s
Z0 = ρ × c                    ρ = Z0 ⁄ c                    c = Z0 ⁄ ρ
Acoustic impedance of air Z0 = 413 Ns/m at 20°C.
Density of air ρ = 1.204 kg/m³ at 20°C.
Temperature Dependence of Physical Quantities 

Sound pressure is not intensity
Differentiate: Sound pressure p is a "sound field size" and sound intensity I is a "sound energy size". In teachings these terms are not often separated sharply enough and sometimes are even set equal. But I ~ p2.

Changing of sound power with distance is nonsense

Question: How does the sound power decrease with distance"? Answer: "April fool - The sound power does not decrease (drop) with distance from the sound source."
Levels of sound pressure and levels of sound intensity decrease equally with the distance from the sound source.
Sound power or sound power level has nothing (!) to do with the distance from the sound source.
Thinking helps: A 100 watt light bulb has in 1 m and in 10 m distance really always the same 100 watts, which is emitted from the lamp all the time. Watts don't change with distance.

A frequent question: "Does the sound power depend on distance?" The clear answer is: "No, not really."
We consider sound fields in air which are described by the scalar quantity p (sound pressure) and the vector quantity v (sound velocity) as sound field quantities.

Acoustic Units of Measurement

 Sound Quantity   Name   Abbreviation   Basic Units   
 1) Wavelength λ  metre  m  m  
 2) Frequency f  hertz
 1/s  cycles per second 
~) 1 kHz = 1000/s 
 3) Period T  second
 s  1 ms = 10−3
 4) Speed of sound c   metre/second   m/s  m/s  
 5) Sound pressure p   pascal
 Pa = N/m2
 kg/m·s2  newton/m2
 1 µPa = 10−6 Pa
 6) Sound intensity I  watt/m2  W/m2  kg/s3  joule/s·m2
 7) Sound power Pac  watt  W  kg·m2/s3  joule/s

Attributes of Sound

 Physical  Perceptual 
 amplitude   loudness
 frequency  pitch
 spectrum  timbre
 duration   length 
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