conversion of sound units - SPL sound level to dB sound pressure unit decibel sound intensity level ratio Pa kPa acoustic energy power convert decibels to pascals audio engineering sound pressure is the effect - sengpielaudioPageRank Checking Icon
 
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Conversion of sound units (levels) 
Sound pressure level SPL to sound pressure p and sound intensity I
Sound pressure to sound level, sound intensity to sound intensity level
Converting decibels (dB) to pascals (Pa) or watts per square meter
 
Conversion of voltage to voltage level
Conversion of factor, ratio, or gain to a level value (gain decibels dB)
Conversion of sound power level to sound pressure level

 
Sound level L  dB (SPL)   | Sound pressure p  Pa  | Sound intensity I  W/m² 
   |    |  
        |         |       
   |    |  
 Sound pressure p  Pa  | Sound level Lp  dB (SPL)   | Sound level LI  dB (SIL)
Sound intensity I  W/m2  | Sound propagation in air  |  
 

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.
Sound pressure or acoustic pressure is the local pressure deviation from the ambient
(average, or equilibrium) atmospheric pressure caused by a sound wave. The sound
pressure
p are the pressure fluctuations in air that the static air pressure is superimposed.
 
The standard atmospheric pressure is 101,325 pascals = 1,013.25 hPa = 101.325 kPa
1,000,000 µPa = 1 Pa = 1 N/m294 dBSPL (and 1 bar = 105 Pa)

20,000,000 µPa = 20 Pa = 20 N/m2120 dBSPL
1 µPa = 10−6 Pa = 10−6 N/m2−26 dBSPL
1 kPa = 103 Pa = 1,000 Pa = 1,000 N/m2154 dBSPL
SPL = Sound Pressure Level          (SIL = Sound Intensity Level)
 
 
 
Sound pressure p (RMS) 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 I 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.
 
Sound pressure p = √ (I × Z0)   Sound intensity I = p2 / Z0     acoustic impedance Z0 = 400 N·s/m3 
 

What does sound level mean?

A reduction of the sound power level of the sound source by 6 dB is resulting in a reduction of the sound
pressure level and the sound intensity level at the location of the receiver by also 6 dB, even if the sound
power drops to a factor of 0.25, the sound pressure dropsto a factor of 0.5 and the sound intensity drops
to a factor of 0.25. The reference value for the sound level was chosen so that with a characteristic
acoustic impedance of
Z0 = ρ · c = 400 N·s/m3 the sound intensity level results in the same value as the
sound pressure level. We therefore simply speak of the "sound level" and leave it open whether sound
pressure level or sound intensity level is meant.

 
 
Sound engineers and sound designers ("ear people") think by the short word
"
sound level" simply of "sound pressure level" (SPL) as sound field quantity.
 
Acousticians and sound protectors ("noise fighters") mean by the short word
"
sound level" probably "sound intensity level" as sound energy quantity.
Equating sound pressure with sound intensity must cause problems.   I ~ p2.
 
 
 
Sound pressure and
Sound pressure level 


       sound pressure 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). 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.
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 quantity. 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. It is wise to use the sound pressure p in Pa or the sound pressure level SPL in dB.
 
The sound pressure or acoustic pressure (alternating pressure changes) is a
dynamic pressure. However, the air pressure (atmospheric equal pressure) is
a static pressure. The dynamic sound pressure is superimposed on the static
air pressure (atmospheric pressure).

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. Sound level is given in dB (decibel).
 
 
To use the calculator, simply enter a value.
The calculator works in both directions of the sign.

Sound field quantity   Sound energy quantity
Sound pressure p (air)
Pa (pascal) 
 ↔  Sound intensity I (air)
W/m2
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 (SPL 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 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 power − Effect and Cause

Note! Since the sound power level is difficult to measure, it is common
to use sound pressure level (SPL) measured in decibels instead.
Doubling the sound pressure raises the sound pressure level by 6 dB.
 
Subjectively perceived loudness (volume),
objectively measured sound pressure (voltage), and
theoretically calculated sound intensity (acoustic power)
 
Psychoacoustic: Relationship between phon and sone

Sound level change and the ratio (gain)

Be precise: 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.

Factor, ratio, and gain
Ratio x for loudness (volume) 
times (sensation)
 ↔  Level change Δ Lloud (psychoacoustics)
dB
Factor loudness   Loudness level= 33.22log (x)
Ratio y for sound pressure (voltage)
times (field quantity)
 ↔  Level change Δ Lp (pressure level)
dB
Sound pressure ratio     Sound pressure level
Ratio z for acoustic intensity (power)
times (energy size)
 ↔  Level change Δ LI (intensity level)
dB
Acoustic intensity     Acoustic intensity level
 
How many decibels is the ratio 1.4142 for the sound pressure?
 
Sound pressure and Sound power − Effect and Cause
 
What is amplitude?
 
Many Amplitudes − The sound field quantities of a plane wave

Sound pressure level SPL and sound pressure

"Sound level" is the sound pressure level in dB SPL or the sound intensity level in dB SIL. For Pa say,
Pascal. This is the size for the pressure
p = force F by area A. The reference sound pressure is
p0 = 20 µPa = 2×10−5 Pa. The reference sound intensity is I0 = I0 = 10−12 W/m2.
 
DAGA and also DIN request the indication of the sound level in dB alone. The attached SPL comes
from the United States and is frowned by acousticians.

 
The often used term "intensity of sound pressure" is not correct. Use "magnitude", "strength", "power",
"effectiveness", "
amplitude" or "level" instead. "Sound intensity" is sound power per unit area, while
"pressure" is a measure of force per unit area. Intensity as sound energy quantity is not the same as
pressure as field quantity.

Sound pressure is not intensity

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

 
 
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.

Comparison of sound pressure level SPL and sound intensity level

Formula for level
 
Note: Membranes (diaphragms) of microphones and our eardrums are
moved by
sound pressure deviations, that is a sound field quantity.
However, the
sound intensity is a sound energy quantity.

Level calculations - sengpielaudio

Reference values (hearing threshold): p0 = 20 Pa = 2 × 10−5 Pa or also I0 = 10−12 W/m2.

The sound pressure is always the sound excess pressure as RMS value.

Compare sound power level and sound pressure level in a distance

Table of Sound Pressure and Sound Intensity Levels

sengpielaudio

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 pressure p (in air)  
Pa = N/m2
 ↔  Sound pressure level Lp 
dB-SPL 
Formel Schalldruck   Schalldruckpegel
Reference sound pressure p0 = 20 μPa = 2 × 10−5 Pa ≡ 0 dB

Sound under water, scroll to bottom.

 
Sound intensity I  
W/m2
 ↔  Sound intensity level LI  
dB-SIL 
Sound intensity   Sound intensity level
Reference sound intensity I0 = 10−12 W/m2 ≡ 0 dB
To speak of the intensity of the sound pressure is nonsense.
Sound pressure and sound intensity are really not the same.
Do not abuse the word "intensity", unless you really mean the
"sound power per area" as W/m.
Use "magnitude", "strength", 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.

"Amplitude" belongs more to the sound field quantities.
 
Sound intensity = sound pressure × particle velocity
Sound i
ntensity = (force / area) × (particle displacement / time)
Sound i
ntensity = sound energy / (area × time) = sound power / area.
I = p × v = (F / A) × (ξ / t) = E / (A × t) = Pac / A.
 
 
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.

There is no "dBA" entry for the threshold of human hearing.
For white noise in the audio band from 20 Hz to 20 kHz, the
difference between dB and dBA is about 2 dB.

 
 

 
Pro audio equipment often lists an A-weighted noise spec – not
because it correlates well with our hearing − but because it can
"hide" nasty hum components that make for bad noise specs.

 
Words to bright minds: Always wonder what a manufacturer
is hiding when they use A-weighting.
*)
 

 
*) 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.
 
Distance law 01
 
Distance law 02.gif
 
Distance law 03.gif
 
The behavior is not inverse-square, but r is inverse-proportional: p ~ 1 / r.
 
                    Intensity-distance
From this follows sound pressure-distance
LittleManBulb
 
Intensity = power / area
I = P/A = P/(4πr2)
Level damping is 6 dB
per distance doubling
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
 
The threshold of pain is known in acoustics as the lowest strength of a stimulus, that is perceived by
the ear as painful. Because of the different sensitivity of people it cannot be given an accurate value.
 
Permissible Exposure Time Guidelines –
Sound Pressure Level - SPL (Dose)
 
How long can a person endure a certain noise level before hearing impairment occurs?
 
 Sound Pressure Level   Sound pressure   Permissible Exposure Time 
115 dB 11.2 Pa 0.46875 minutes (~30 sec)
112 dB 7.96 Pa 0.9375 minutes (~1 min)
109 dB 5.64 Pa 1.875 minutes (< 2 min)
106 dB 3.99 Pa 3.75 minutes (< 4 min)
103 dB 2.83 Pa 7.5 minutes
100 dB 2.00 Pa 15 minutes
  97 dB 1.42 Pa 30 minutes
  94 dB − − − − − − − − − − 1.00 Pa − − − − − − 1 hour − − − − − − − − − − − − − −
  91 dB 0.71 Pa 2 hours
  88 dB 0.50 Pa 4 hours
  85 dB 0.36 Pa 8 hours
  82 dB 0.25 Pa 16 hours
 
Accepted guidelines for recommended permissible exposure time for continuous time
weighted average noise, according to NIOSH-AINSI and CDC.
For every 3 dB sound pressure level (SPL) over 85 dB, the permissible exposure time is cut
in half − before damage to our hearing can occur.
NIOSH = National Institute for Occupational Safety and Health and
CDC = Centers for Disease Control and Prevention.
OSHA = Occupational Safety and Health Administration.
NIOSH represents the use of an 8-hour exposure of noise at 85 dBA and a 3 dBA doubling
rate, to determine the noise dose.
OSHA represents the use of an 8-hour exposure of noise at 90 dBA and a 5 dBA doubling
rate, which does not protect many workers from hearing loss over their whole working
lifetime.
This may not represent a worldwide view of the subject.
Noise is an increasing public health problem and can have the following adverse health
effects: hearing loss, sleep disturbances, cardiovascular and psychophysiological problems,
performance reduction, annoyance responses, and adverse social behaviour.
A person feels and judges sound events by exposure time, spectral composition, temporal
structure, sound level, information content and subjective mental attitude.

To determine SPL and exposure time
To use the calculator, simply enter a value.
The calculator works in both directions of the
sign.

 
Sound pressure level (SPL) 
94 dB + dB
 ↔  Permissible exposure time 
 minutes
 
Conversion: sound pressure, particle velocity, acoustic impedance, and intensity
 
Table of sound levels (pressure and also intensity)

Sound Field quantities    AnimatedLaughingSmiley
Sound pressure, sound or particle velocity,
particle displacement or displacement 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 fluctuation 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
eardrums. In stereo history the level differences have been called "intensity" differences,
but sound intensity is a specifically defined size 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.
 
conversion of sound units - sound level, sound pressure, sound intensity - sengpielaudio

Important to notice: 1 Pa = 1 N/m294 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 size 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 size. Write out the word "decibel" for such applications, and be sure that the word 'decibel' follows, not precedes the description of the relevant acoustical size.
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 Pa 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 size decreases with 1/r2.
I is proportional to p2.
Sound field parameters: Sound pressure, sound (particle) 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" stereophonc system does not work with sound intensities but is working with
linear sound pressure differences. What moves the microphone's diaphragms and also our
eardrums? It is simply the sound pressure and not the sound intensity.
The sound pressure is the function of the time and place of the sound pressure fluctuations Δ
p
as an overlay to the atmospheric pressure. The sound pressure effect is moving our eardrums
and is therefore relevant to the perception of sound.
 
Relationship of acoustic quantities (sizes)
 
Levels and References of Sound Quantities - Conversions, Calculations, and Formulas
 
Comparative representation of sound field quantities and sound energy sizes

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. size 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 fluctuations 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 size.

 

Sound pressure and sound power
 
Correlation of volume and loudness − sone and phon
 
conversions and Calculations - Sound sizes 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.

Correct version Wrong expression
Sound pressure (amplitude) falls inversely
proportional to the distance 1/r from the sound source.

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

Sound pressure is not intensity

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.
 
 
Differentiate: Sound pressure p is a "sound field quantity" and sound
intensity I is a "
sound energy quantity". 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 a sound field quantity.

 

Sound pressure and sound level under water

To use the calculator, simply enter a value.
The calculator works in both directions of the
sign.

Sound under water
Sound pressure p (under water)
Pa = N/m2
 ↔  Sound pressure level Lp (under w.)
dB-SPL 
Sound pressure   Sound pressure level
Reference pressure p0 = 1 μPa = 1 × 10−6 Pa ≡ 0 dB (different to air)
Conversion of dB between air to water

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.
Furthermore, airborne sound pressure levels are often referred to as frequency-weighted
sound pressure level indicated by the frequency response of human hearing. For the
evaluation of the influence of underwater sound on marine animals there is no useful
reference scale. The difficult comparison of noise data in air and in water provides sound
in discussions about the harm of sonars and echo sounders and sounds of marine animals
always show confusion. The most important measure of the sound of water is used as the
sound produced by the sound pressure level (SPL). Although formally the same methods
can be employed for water noise and air noise it is difficult to be compared and lead to
serious misunderstandings. Levels are logarithmic values and interpret meaningful values
only if the reference values used in each case be respected.
The reference value for the sound pressure level in air is selected at 20 µPa, the reference
sound of water on the other hand is 1 µPa. The reference value for airborne sound has
been selected on the basis of the human hearing threshold and corresponds to a plane
wave propagation in the medium of air to a sound pressure of about 2×10−5 pascals (20
µPa). The reference sound pressure corresponds to a sound intensity of about 10−12
W/m. Water is much harder than air, so much for the same intensity of the acoustic
particle velocity is less relevant, but the sound pressure is greater. For this reason, a
comparison of the sound pressure is not useful anyway. If you want to compare the energy
flux density (intensity) should be used. Because the measured sound pressure is
technically more accessible, we take it anyway. The intensity of the underwater sound in
which used therein reference pressure of 1 µPa corresponds to an intensity of about
0.65×10−18 W/m. The relationship between sound pressure and sound intensity are also
a part of air pressure, depending on its temperature and salinity of the water.
Approximately the same level of detail for air and water at their respective reference
pressure in level differ by approximately 62 dB.
For a comparability of the levels - anyway in question - withdraw from the pressure
level under water about 62 dB.

The large difference between the level of sound in air and the indication of the sound level
under water specified in decibels (dB) is seldom recognized and clearly explained.

How is sound in water different from sound in air?
How does sound in air differ from sound in water?

Comparing sound levels in air against sound levels in water must be done very carefully. First, by
accepted convention, the reference pressure values are different by 26 dB. Second, due to the
difference in impedance (the stiffness or density of the medium) between air and water, roughly a
3,500 times greater power level (36 dB) is required in air to produce an equivalent pressure level
in water. Combining these two values, a 26 dB + 36 dB = 62 dB difference, or correction factor,
between the two scales is required. Therefore, 62 dB must be subtracted from a sound level in
water to produce an equivalent acoustic intensity in air. It is misleading to compare the decibels of
the underwater sound with the decibels of sounds heard in the 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 fluctuations
(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
The advice to use a soundfield microphone for a surround sound recording under water with a
condom, had to be recognized as nonsense, since the four necessary pressure gradient
microphones lose completely the effect.
 
 
 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.

Weighted Sound is not given in phon, but in dB(A).

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 (hearing threshold)
Reference sound intensity level LI0 = 0 dB-SIL (hearing threshold)
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 Pa = 2×10−5 Pa (hearing threshold)
Reference sound pressure level Lp0 = 0 dB-SPL (hearing thresholdl)
Get sound pressure p when entering sound pressure level Lp:
p = p0×10(Lp/20) in Pa (= N/m2) = 210−5×10(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 = 20log (p / 210−5) 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 size.)
(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.
 
What is the highest sound pressure possible?
How many decibels is the loudest noise?
 
A typical false statement: "No noise levels can exceed 194 dB ever." Is the
end at 194 dB? In addition to this perception threshold is discussed more
often a physical limit to 194 dB. Sound is nothing more than a minor
disturbance of air pressure and 194 dB is theoretically the same as the
disturbance itself. It must be distorted. Even louder noise is possible, but
heavily distorted. That's chaos.
This high sound pressure will break all measurement microphones and
human beings are completely torn when they are close to the center of a
nuclear explosion. No hearing protection (ear muffs or ear plugs) can help
you there.
 
Some information about Hearing Level (HL)
Pure-tone audiometric thresholds are expressed in dB HL.
 
Frequency  dB SPL   dB HL 
  250 Hz  +15.0     0.0
  500 Hz    +9.0     0.0
1000 Hz    +3.0     0.0
2000 Hz    −3.0     0.0
4000 Hz    −4.0     0.0
8000 Hz  +13.0     0.0

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