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Fill in the gray top box and click on the calculation button. 1 Pa = 1 pascal = 1 N/m2.
The atmospheric pressure is not the same as the sound pressure.
The standard atmospheric pressure is 101,325 pascals = 1,013.25 hPa = 101.325 kPa
• 1,000,000 µPa = 1 Pa = 1 N/m2 ≡ 94 dBSPL and 1 bar = 105 Pa
1 kPa = 103 Pa = 1000 Pa = 1,000 N/m2 ≡ 154 dBSPL
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Sound pressure and Sound power – Effect and Cause
| Note! Since the sound intensity level is difficult to measure, it is common to use sound pressure level measured in decibels instead. Doubling the Sound Pressure raises the Sound Pressure Level by 6 dB. |
Sound level change and the ratio
Double the sound pressure and double the sound power or double the acoustic intensity
| To use the calculator, simply enter a value. The calculator works in both directions of the ↔ sign. |
How many decibels is the ratio 1.4142 for the sound pressure?
Sound pressure and Sound power – Effect and Cause
Sound pressure level and Sound pressure
"Sound level" is the sound pressure level in decibel (SPL), or sometimes the acoustic 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.
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 (loudness) is determined mostly by the sound pressure p and expressed as sound pressure level Lp in dB. 
Note: The sound intensity is a sound energy quantity. Membranes (diaphragms) of microphones and our eardrums are moved by alternating sound pressure, that is a sound field quantity. |
Reference values (threshold of hearing): p0 = 20 µPa = 2 × 10−5 Pa (I0 = 10−12 Watt/m2)
The sound pressure is always the sound excess pressure as RMS value.
Compare sound power level and sound pressure level
Table of Sound Pressure and Sound Intensity Levels
Sound pressure, Sound intensity and their Levels
| To use the calculator, simply enter a value. The calculator works in both directions of the ↔ sign. |
Sound under water, scroll to bottom.
| Use "magnitude", "strength", "amplitude", or "level" instead. "Sound intensity" is sound power (acoustic power) per unit area, while "pressure" is a measure of force per unit area. Intensity is not equivalent to pressure. |
| Note - Comparing dB and dBA: There is no conversion formula for measured dBA values to sound pressure level dBSPL or vice versa. |
| The auditory threshold at 0 dBSPL without weighting cannot be the same as 0 dBA with dBA-weighting for broadband noise. Only for a pure tone of 1 kHz both values can be set equal. |
– not because it correlates well with our hearing – but because it
can "hide" nasty hum components that make for bad noise specs. |
*) http://www.google.com/search?q=Always+wonder+what+a+manufacturer+Rane&filter=0
The sound pressure p decreases with 1/r from the sound source.
The behavior is not inverse-square, but r is inverse-proportional: p ~ 1 / r.
|
| Intensity = power / area I = P/A = P/(4πr2) Level damping is 6 dB per r |
See also: Weighting filter- calculation frequency f to dBA
What is the threshold of pain?
You can find the following rounded values in various audio articles:
| Sound pressure level Lp |
Sound pressure p |
| 140 dBSPL | 200 Pa |
| 137.5 dBSPL | 150 Pa |
| 134 dBSPL | 100 Pa |
| 120 dBSPL | 20 Pa |
| Conversion: sound pressure, particle velocity, acoustic impedance, and intensity Table of sound levels (pressure and also intensity) |
Sound Field Quantities
 Sound pressure, sound or particle velocity, particle displacement or particle amplitude, (voltage, current, electric resistance). Inverse Distance Law 1/r |
Sound Energy Quantities Sound intensity, sound energy density, sound energy, acoustic power. (electrical power). Inverse Square Law 1/r² |
| Sound (or acoustic) pressure is the change in pressure caused by a sound (acoustic)
wave. Sound power (or acoustic energy) is the amount of energy contained in a sound
(acoustic) wave.
It's unfortunate that the terms 'power' and 'energy' get so badly intermixed in acoustics. They really aren't the same thing at all. Energy is the capacity to 'do' something. Power is the amount of energy used (or generated) per unit of time. |
| Hearing is directly sensitive to sound pressure. Only the sound pressure moves our
ear drums. In stereo history the level differences have been called "intensity" differences,
but sound intensity is a specifically defined quantity and cannot be sensed by a simple
microphone, nor would it be of value in music recordings if it could be. "Intensity" stereophony is better termed as level difference stereophony. |
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Important to notice: 1 Pa = 1 N/m2 ≡ 94 dB and 1 bar = 105 Pa.
| ASACOS Rules for Preparation of American National Standards in ACOUSTICS, MECHANICAL VIBRATION AND SHOCK, BIOACOUSTICS, and NOISE states:
3.16 Unit symbols - 3.16.1 When to use unit symbols in the text of the standard, the unit symbol for a quantity shall be used only when the unit is preceded by
a numeral. When the unit is not preceded by a numeral, spell out the name of the unit. In text, even when a numerical value is given, it is desirable to spell out
the name of the unit. Moreover, the name shall be spelled out when it first appears in the text, and more often if the text is lengthy. Thus, in text write "...a
sound pressure level of 73 dB; or "...a sound pressure level of 73 decibels." Do not write "sound pressure level in dB"; the correct form is "sound pressure level
in decibels." Do not write "dB levels", "dB readings", or "dB SPL". Levels or readings are not of decibels; they are of sound pressure levels or some other
acoustical quantity. Write out the word "decibel" for such applications, and be sure that the word 'decibel' follows, not precedes the description of the relevant
acoustical quantity. The guidelines given for the National Standards clearly excludes the use of "dB SPL". The reference added to the decibel article ends up being a document that merely includes "dB SPL" in a list of terms. The glossary within the same document does not even list this supposed term, even though weighted decibel terms are defined. The glossary in the file does have an entry for "sound pressure level': (1) Ten times the logarithm to the base ten of the ratio of the time-mean-square pressure of a sound, in a stated frequency band, to the square of the reference sound pressure in gases of 20 micropascals (µPa). Unit, dB; symbol, Lp. (2) For sound in media other than gases, unless otherwise specified, reference sound pressure in 1 µPa (ANSI S1.1-1994: sound pressure level). A reference level of 20 µPa is often used. In general, it is necessary to know the reference level when comparing measurements of SPL. The unit dB (SPL) is often abbreviated to just "dB", which gives some the erroneous notion that a dB is an absolute unit by itself. |
| How does sound level depend on distance from the source? Damping of sound level with distance from sound source http://www.sengpielaudio.com/calculator-distance.htm |
|
Intensity I is defined as the power per unit area. The surface area of the sphere is A = 4 π r2, so the sound power P passing through each square metre of surface is the intensity: I = P / A = P / 4 π r2. We see that, for a uniformly radiating sound source, sound intensity is inversely proportional to the square of the distance r away from the source: I2 / r12 = I1 / r22. But sound intensity is proportional to the square of the sound pressure, so we could equally write: p2 / p1 = r1 / r2. We see that sound pressure falls inversely proportional to the distance r away from the source. If we double the distance, we reduce the sound pressure by a ratio of 2 and the sound intensity by a ratio of 4. In other words, we reduce the sound level by (−)6 dB. |
| Often it is confusing that the sound pressure p as a sound field quantity decreases with 1 / r of
the distance but the sound intensity I as a sound energy quantity decreases with 1/r2. I is proportional to p2. Sound field parameters: Sound pressure, sound velocity, particle displacement. These terms are all proportional to the electric voltage, electric current, and the electrical resistance. Sound energy parameters: Sound intensity, sound energy, sound energy density, sound performance. To all this, the power is proportional. Intensity is called colloquially the way in which something is operated: intense, driven, focused. Intensity is, however, especially in physics and acoustics, and it is important technical term for the energy alone. The word intensity is quite often incorrectly used for strength, force, amplitude and level. Therefore, the term intensity should be taken only if really the (radiation) energy is meant. In sound recording technology with microphones it is almost always the strength, the amplitude or the level that is meant and only as a rare exception the sound intensity (energy) is wanted. Even the "intensity" stereophony system does not work with the sound intensities but is workung with linear sound pressure differences. What moves the microphone's diaphragms of our ear drums? It is simply only the sound pressure and not the thoughtless sound intensity. The sound pressure is the function of the time and place of the sound pressure change Δ p as an overlay to the atmospheric pressure. The sound pressure effect is moving our ear drums and is therefore relevant to the perception of sound. |
Sound pressure and Sound power – Effect and Cause
Sound Level Comparison Chart
| Table of sound level dependence and the change of the respective ratio to subjective loudness (volume), objective sound pressure (voltage), and sound intensity (acoustic power). How many decibels (dB) level is double, half, or four times as loud? How many dB to appear twice as loud? Here are all the different ratios. |
| 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. quantity | Psycho quantity | Field quantity | Energy quantity |
| 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. |
|
Sound level, loudness, and sound pressure are not the same things. There are variations in individual perception of the strength of sound. The sound pressure measured twice as much gives 6 dB more level. The sound perceived twice as loud needs roughly a sound level increase by 10 dB. The human perception of loudness is perceived differently from each subject. In other words it is one's own perception of sound and it is subjective of sound pressure level SPL. |
| Notice - The sound pressure as sound field quantity is not the same as the sound intensity as sound energy quantity. |
Sound pressure and sound power
Correlation of volume and loudness − sone and phon
Conversions and Calculations - Sound Quantities and their Levels
Frequently used false statements in the context of
sound values and the distance of the sound source
The sound pressure decreases from a point source with 1/r after the distance law.
| 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. |
| 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. |
| The sound power level or the sound power is firmly committed to the sound source and is really independent from the distance. |
Sound pressure and sound level under water
| To use the calculator, simply enter a value. The calculator works in both directions of the ↔ sign. |
| In 1970, the pressure reference level of 0 dB ≡ 1 µPa was chosen by the US Navy for their
underwater work for sound in water. For an identical source intensity in water and air, the sound pressure generated in water will be about 60 times greater than in air. |
| Microphones that are used under water are called hydrophones. It is possible to get these special
microphones at the firm DPA. Usual Microphones must be protected from water. Imaginative engineers on location draw a condom on conventional microphones, when recording in the situation of rain or under water in a swimming pool. This is no joke. The slack latex skin seals the microphone capsule from water and the sound pressure changes (scalar) are transmitted - but this trick is applicable only for pure pressure receivers, that means when microphones are omnidirectional. That does not work with pressure gradient microphones like cardioids, because the motion of the pressure gradient, that is the pressure difference before and behind the diaphragm as a vector, is horribly disturbed by the condom. In the "YouTube" tips making microphones watertight or waterproof, they forget to explain that this really does not work correctly for cardioid microphones, and other pressure gradient microphones. They don't know it better; see: YouTube: Waterproofing a microphone with a condom |
| Note: Only microphones with omnidirectional polar patterns work correct with condoms under water. |
| Calculations and conversions of pressure units More conversions of pressure and stress units Conversions of pressure units |
| Question: What is the standard distance to measure sound pressure level away from equipment? There is no standard distance. It depends on the size of the sound source and the sound pressure level. |
Relationship between Sound Pressure and Sound Power
Sound Power and Pressure Measurements
| How does the sound decrease with distance? |
| Conversion of sound units Sound intensity: Reference sound intensity I0 = 10−12 W/m2 (Threshold of hearing) Reference sound intensity level LI0 = 0 dB-SIL (Threshold of hearing level) Get sound intensity I when entering sound intensity level LI: I = I0×10^(LI/10) in W/m2 = 10−12×10^(LI/10) in W/m˛. Get sound intensity level LI in dB when entering sound intensity I in W/m2. LI = 10×log (I / I0) in dB = 10×log (I / 10−12) in dB. Sound pressure: Reference sound pressure p0 = 20 µPa = 2×10−5 Pa (Threshold of hearing) Reference sound pressure level Lp0 = 0 dB-SPL (Threshold of hearing level) Get sound pressure p when entering sound pressure level Lp: p = p0×10^(Lp/20) in Pa (= N/m2) = 2×10−5×10^(Lp/20) in Pa (N/m2). Get sound pressure level Lp in dB when entering sound pressure p in Pa: Lp = 20×log (p / p0) in dB = 20×log (p / 2×10−5) in dB. How to add two sound intensity levels LI1 = 50 dB and LI2 = 65 dB? Get out of dB and back to ratio. (Energy quantity.) (The reference sound intensity is not used here.) I1 = 10^(LI1/10) = 10^(50/10) = 100000. I2 = 10^(LI2/10) = 10^(65/10) = 3162277. Add them to get I = I1 + I2 = 3262277. Now get back to dB: LI = 10×log (3262277) = 65.13 dB. For large dB differences over 10, just take the highest value. How do you add two sound pressure levels Lp1 = 50 dB and Lp2 = 65 dB? Get out of dB and back to ratio. (Field quantity.) (The reference sound pressure is not used here.) p1 = 10^(Lp1/20) = 10^(50/20) = 316. p2 = 10^(Lp2/20) = 10^(65/20) = 1778. Pythagoras: p = √ (p12+p22) = √ (3162 + 17782) = 1806. Now get back to dB: Lp = 20×log (1806) = 65.13 dB. For large dB differences over 10, just take the highest value. |
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