The relation of sound sizes values calculator sound pressure level sound acoustic power level intensity level particle velocity energy amplitude acoustics formulas decubel reference dB - sengpielaudio
 
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● Levels and References of the Sound  Quantities ●
 
Conversions, Calculations, and Formulas
 
 
Sound pressure as Sound field quantity:
The auditory threshold is used as the reference sound pressure p0 = 20 µPa = 2 × 10−5 Pa.
The threshold of hearing corresponds to the sound pressure level Lp = 0 dB at f = 1 kHz.
 
Sound intensity as Sound energy quantity:
The auditory threshold is calculated as the reference sound intensity I0 = 10−12 W/m2.
The threshold of hearing corresponds also to the sound intensity level LW = 0 dB at f = 1 kHz.
 
Readings of a pure 1 kHz tone should be identical, whether weighted or not.
 
The following calculator shows the often desired direct conversion of sound pressure to sound intensity and vice versa.
 
 
Simply enter the value to the left or the right side.
The calculator works in both directions of the ↔ sign.

Sound pressure p: (air)
Pa 		 ↔  Sound intensity I: (air)
W/m2
Formel   Formel
Standard reference sound pressure p0 = 20 μPa = 2 × 10−5 Pa      Pa = N/m2
Standard reference sound intensity I0 = 1 pW/m2 = 10−12 W/m2      Z0 = 400 N·s/m3
Sound pressure p = √ (I × Z0)      Sound intensity I = p2 / Z0

Sound pressure p: 
Pa = N/m2		  ↔  Sound pressure level Lp:
dB-SPL
Formula   Formula
Sound field size
Standard reference sound pressure p0 = 20 μPa = 2 × 10−5 Pa ≡ 0 dB

Acoustic intensity I: 
W/m2		  ↔  Sound intensity level LI:
dB-SIL
Formula   Formula
Sound energy size
Standard reference sound intensity I0 = 1 pW/m2 = 10−12 W/m2 ≡ 0 dB

Acoustic power Pac:
W		  ↔  Sound power level LPac:
dB-PWL
Formula   Formula
Sound energy size
Standard reference sound power Pac0 = 1 pW = 10−12 W ≡ 0 dB

There is also the reference power P0 = 1 milliwatt = 0.001 watt ≡ 0 dBm.

Particle velocity v: 
m/s		  ↔  Particle velocity level Lv:
dB-SVL
Formula   Formula
Sound field size
Standard reference particle velocity v0 = 5 × 10−8 m/s ≡ 0 dB

Sound energy W: 
J = W·s		  ↔  Sound energy level LW:
dB-SWL
Formula   Formula
Sound energy size
Standard reference sound energy W0 = 1 pJ = 10−12 J ≡ 0 dB   J = W·s

Sound energy density E: 
J/m3 = W·s/m3		  ↔  Sound density level LE:
dB-SEL
Formula   Formula
Ref. Sound energy density E0 = 1 pJ/m3 = 10−12 J/m3 ≡ 0 dB   (W·s/m3)

Sound sizes: Differentiate between sound field sizes and sound energy sizes

Sound Field sizes    That's good!
Sound pressure, sound or particle velocity,
particle displacement or particle amplitude,
(voltage, current, electric resistance).
Inverse Distance Law 1/r		          Sound Energy sizes
Sound intensity, sound energy density,
sound energy, acoustic  power.
(electrical power).
Inverse Square Law 1/r²

Since sound measuring instruments (meters) respond to sound pressure the "decibel" is generally associated with sound pressure level. Sound pressure levels quantify in decibels the strength (not intensity!) of given sound sources. Sound pressure levels vary substantially with distance from source, and also diminish as a result of intervening obstacles and barriers, air absorption, wind and other factors.
Sound Pressure Level (SPL): 20×log (p/p0) = 10×log (p/p0)2, where  p0 = 2×10−5 N/m2. p = root mean square sound pressure  (N/m2 = Pa).
The usual reference level p0 is 20×10−6 Pa, the auditory threshold. Note that the noise from motors is documented in sound power (acoustic power) level. "Threshold of
audibility" or the minimum pressure fluctuation detected by the ear is less than 10−9 of atmospheric pressure or about 2×10−5 Pa (pascal) at 2000 Hz. "Threshold of pain" corresponds to a pressure 106 times greater, but still less than 1/1000 of atmospheric pressure.
The standard air pressure is 101325 Pa = 101.325 kPa or 1013.25 hectopascal.
Because of the wide range, sound pressure measurements are made on a logarithmic decibel scale.
Sound power levels are connected to the sound source and are independent of distance. Sound power levels are indicated in decibels. Lw = 10×log (P / P0) where the reference power P0 = 10−12 W, calculated from p0 = 20 micropascals, which is the lowest sound persons of excellent hearing can discern. Sound power is measured as the total sound power emitted by a source in all directions in watts (joules / second).
Sound power levels do not vary with distance from source.

Questions:
1. How many decibels (dB) is the sound pressure p = 1 Pa?
2. How many decibels (dB) is the acoustic intensity I = 1 W/m2?
3. How many decibels (dB) is the acoustic power Pac = 1 W?
4. How many decibels (dB) is the particle velocity v = 1 m/s?
5. How many decibels (dB) is the sound energy density w = 1 J/m3?
The calculators above can help with the answers.

How many decibels (dB) is the level of the sound energy W = I×t×A in J = W×s?
This question is found quite rarely. For calculations we use more the 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.

 
Note: The radiated sound power (sound intensity) is the cause
and the sound pressure is the effect.
The effect is of particular interest to the sound engineer.
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). As a sound designer you don't need that sound energy size. 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.
 
Who is involved in audio engineering, should care less about the cause of intensity, power and energy, but better care on the effect of the sound pressure and the sound level (sound pressure level SPL) on the eardrums and the microphones, and the corresponding audio voltage or its voltage level.
 

Sound pressure and Sound power − Effect and Cause

Conversion of Factor or Ratio to Level Value (Decibels dB)

Table of Sound Levels, Sound Pressure, and Sound Intensity
 
Conversion of Sound Units (Levels)
 
Damping of Sound Level with Distance

Frequently used false statements in the context of
sound values and the distance of the sound source

Wrong expression Correct version
Sound pressure falls inversely proportional
to the square of the distance 1/r2 from the
sound source.                                                   wrong		 Sound pressure falls inversely proportional
to the distance 1/r from the sound source.
That is the 1/r law or distance law.
Sound pressure level decreases as the
distance increases per doubling of distance
from the source by (−)3 dB.                            wrong		 Sound pressure level decreases by (−)6 dB per
doubling of distance from the source to 1/2 (50 %)
of the sound pressure initial value.
Sound intensity (energy) falls inversely
proportional to the distance 1/r from the sound
source.                                                               wrong		 Sound intensity (energy) falls inversely proportional
to the square of the distance 1/r2 from the sound
source. That is the square law.
Sound intensity level decreases inversely as the
square of the distance increases per doubling of
sound source with (−)3 dB per doubling.       wrong		 Sound intensity level decreases by (−)6 dB per
doubling of distance from the source to 1/4 (25 %)
of the sound intensity initial value.

Neither the sound power nor the sound power level decreases in doubling
the distance. Why is this so?
The sound power level quantifies the totally radiated sound energy from an object.
Different to the sound pressure the sound power is independent of the distance to the sound source, the surrounding area and other influences.
 
Notice: The psychoacoustic subjective sensations of loudness do not
belong to those predictable and measurable sound sizes; 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
 
"Sound level" is the sound pressure level in decibel (SPL), or sometimes the sound intensity level in dB (SIL).
The reference sound pressure is p0 = 20 µPa = 2 × 10−5 Pa − the reference sound intensity is I = 10−12 W/m2.
 
 
Differentiate: Sound pressure p is a "sound field size" and
sound intensity I is a "sound energy size". Amateurs often
think wrongly, that sound pressure and intensity mean the same.
 
 
Notice, that the calculation I ~ p2 is effective for progressive plane waves.
It can be seen that "sound intensity" (acoustic intensity) may never be equated with "sound pressure".
The sound pressure is the alternating sound pressure as RMS value. The sound pressure amplitude
is the peak value of the sound pressure.
The sound volume is determined by the sound pressure p and expressed as sound pressure level Lp in dB.
 
Comparison of sound pressure level SPL and sound intensity level
 
Pegel-Formel
 
Note: The sound intensity is a sound energy size. Membranes (diaphragms) of microphones and our eardrums are moved by sound pressure deviations, that is a sound field size.

Sound Level Comparison Chart and the Ratios

Table of sound level dependence and the change of the respective ratio to subjective volume (loudness), objective sound pressure (voltage), and sound intensity (acoustic power).
How many decibels (dB) level change is double, half, or four times as loud?
How many dB to appear twice as loud (two times)? Here are all the different ratios.
Ratio means "how many times" or "how much" ... Doubling of loudness.
 
Level
Change		 Volume
Loudness		 Voltage
Sound pressure		 Acoustic Power
Sound Intensity
+40 dB 16 100   10000
+30 dB   8    31.6 1000
+20 dB   4 10 100
+10 dB  2.0 = double   3.16 = √10 10
  +6 dB   1.52 times  2.0 = double        4.0
  +3 dB   1.23 times 1.414 times = √2  2.0 = double  
  - - - - ±0 dB - - - - - - - - 1.0 - - - - - - - - - - - 1.0 - - - - - - -   - - - -  1.0 - - - - -  
  −3 dB     0.816 times    0.707 times         0.5 = half 
  −6 dB     0.660 times    0.5 = half 0.25
−10 dB     0.5 = half 0.316    0.1  
−20 dB          0.25 0.100    0.01
−30 dB          0.125 0.0316    0.001
−40 dB          0.0625 0.0100      0.0001
Log. size Psycho size Field size Energy size
dB change Loudness multipl. Amplitude multiplier Power multiplier
 
For a 10 dB increase of the sound level we require ten times more power from the amplifier. This increase of the sound level means for the sound pressure a lifting of the ratio 3.16. Loudness and volume are highly subjective. That belongs to the domain of psychoacoustics.

The standard atmosphere is 101325 Pa = 101.325 kPa or 1013.25 hectopascal.

Comparative representation of sound field sizes and sound energy sizes
 
Relationship of acoustic sizes of a plane progressive acoustic sound wave

Audio voltage and level

Simply enter the value to the left or the right side.
The calculator works in both directions of the ↔ sign.

Voltage V (audio): 
volts		  ↔  Voltage level LU:
dBu
formula 04   formula 05
Reference voltage V0 = 0.7746 Volt ≡ 0 dBu
Voltage V: 
volts		  ↔  Voltage level LU:
dBV
formula 04   formula 06
Reference voltage V0 = 1 Volt ≡ 0 dBV

Unclear equations in books

The sound intensity I in W/m2 in a plane progressive wave is given as:
 
                            Table 01 or also as Table 02
 
But only one equation can be correct.
 
Sometimes, these equations will show further information:
 
                            Table 03 or also as Table 04
 
                            Table 05
 
The tilde will indicate that it is the RMS value and the roof will show that it is the amplitude value, ie, the peak value. For sinusoidal signals, the peak value means the amplitude.
With these more accurate data, both equations are correct. You just need to know exactly whether the peak value or the RMS value is applied.
 
Sound pressure p in Pa = N/m2 − particle velocity v in m/s − acoustic intensity I in W/m2 that is N/m2 · m/s                Energy equivalent: J (joule) = N · m = W · s
 
In audio engineering we always (!) assume RMS values, if not specially noted different. The reference sound pressure is p0 = 20 µPa = 2 × 10−5 Pa and this is the RMS value.
 
What is an Amplitude
 
How does the sound decrease with distance?
How does the noise depend on distance from the source?

 
 The constant unsureness is the answer of the question:
 "How many dBs are doubling a sound"?
 
 Answer: Doubling means the "factor 2". What does doubling of a"sound" mean?
 Twice the (sound) intensity is obtained by an increase of the (sound intensity) level of 3 dB.
 Twice the sound pressure is obtained by an increase of the (sound pressure) level of 6 dB.
 Twice the loudness feeling is obtained by an increase of the (loudness) level of about 10 dB.
 
 
The question: "Is noise level really the sound intensity level?" will be differently answered by musicians and sound engineers than by sound fighters. We measure the noise and 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. Acousticians will have slightly different sights.
 
SPL Meter
 
By the way, sellers always want us to buy a sound pressure level meter with digital display.
But much better, however, is an analogue-to-read display - as in this figure.
If you don't understand: Do you have a wrist watch with good to read analog hands or do you have a digital display there? Why?
 
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