Table chart sound pressure levels SPL normal sound pressure level test noise sound intensity units decibel level decibel comparison chart of common sounds ratio calculation comparison loudness decibel dB scale compression rarefaction conversion of sound pressure to sound intensity ratio factor units - sengpielaudio
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Decibel TableSPLLoudness Comparison Chart 
Table of Sound Levels (dB Scale) and the corresponding
Units of Sound Pressure and Sound Intensity (Examples)
Decibel level and comparison of common sounds

To get a feeling for the heard sound quantities in decibels (dB), look at the table below which gives
values for the
sound levels of common sounds in our environment. Also shown are the corresponding
sound pressures and sound intensities with the absolutely necessary measuring of the distance.
From these we can see that the decibel scale gives numbers in a much more manageable range.
Sound pressure levels are measured without
weighting filters.
Avoid using the psychoacoustical terms loudness perception and volume.
This subjective sound-sensation is not clearly measurable without ambiguity.

The term "loudness" or "volume" is a problem because it belongs to psycho-
acoustics and this personal feeling is not correct definable.

Loudness as a psychological correlate of physical strength (amplitude) is also
affected by parameters other than sound pressure, including frequency,
bandwidth, spectral composition, information content, time structure, and the
duration of exposure of the sound signal. The same sound will not create the
same loudness perception by all individuals (people).

As psycho-acoustic parameters to describe the "loudness" there is the
"loudness level" with the unit phon and the "loudness" with the unit sone.
The values are averaged and can differ about ±10 dB. With sound pressure p is
always meant the root mean square value (RMS) of the sound pressure, without
extra announcement. The amplitude of the sound pressure means the peak value.
The sound pressure (RMS) is the most important quantity in sound measurement.
Our hearing is a
sound pressure receptor, or a sound pressure sensor,
because the eardrums (tympanic membranes) are moved by the sound
pressure as a sound field quantity. That is the important effect of the
excess sound pressure.

It is not an energy receiver! When listening to music, forget the sound intensity as
energy quantity. The perceived sound consists of periodic acoustic pressure
vibrations (sound pressure) which are superimposed on the surrounding static air
pressure of 101 325 Pascal (mean atmospheric pressure).

The sound is the change of sound pressure p, which is measured in pascal.
1 Pa ≡ N/m2 ≡ 1 J / m3 ≡ 1 kg / (m·s2). Usually
p is the RMS value.
Table of sound levels L (loudness of noise) with
corresponding sound pressure and sound intensity
Sound sources (noise)
Examples with distance

   Sound pressure   
 Jet aircraft, 50 m away 140
 Threshold of pain 130
 Threshold of discomfort 120
 Chainsaw, 1 m distance 110
 Disco, 1 m from speaker 100
 Diesel truck, 10 m away 90
 Kerbside of busy road, 5 m 80
 Vacuum cleaner, distance 1 m  70
 Conversational speech, 1 m 60
 Average home 50
 Quiet library 40
 Quiet bedroom at night 30
 Background in TV studio 20
 Rustling leaves in the distance 10
 Hearing threshold  0
    Sound pressure p
N/m² = Pa
     Sound field quantity     
Sound intensity I
Sound energy quantity
  200   100
    63.2   10
    20   1
      6.3   0.1
      2   0.01
      0.63   0.001
      0.2   0.000 1
      0.063   0.000 01
      0.02   0.000 001
      0.006 3   0.000 000 1
      0.002   0.000 000 01
      0.000 63   0.000 000 001
      0.000 2   0.000 000 000 1
      0.000 063   0.000 000 000 01 
      0.000 02   0.000 000 000 001 
Wrong question: "Jackhammer. How many dBs?" The distance is missing!
Notice: A given sound level without a given distance is really useless.
A typical question: How "loud" is 15 dB? Is there a distance from the source?
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 drops to 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.
The sound level depends on the distance between the sound source and
the place of measurement, possibly one ear of a listener.

The sound pressure level Lp in dB without the given distance r to the sound
is meaningless. Unfortunately this error (unknown distance) is often
to find. Many users really wrongly believe that a sound source must have a
fixed dB value; e.g. jackhammer = 110 dB and jet plane = 130 dB.
Distance ??? No distance, then forget the decibel value!

The threshold of pain, depending on the frequency composition and the
sensitivity of the tested person, is to find between 120 dB and 140 dB.

There is no noise decrease or sound drop per meter.
We get a sound level drop of 6 dB per doubling of distance.
 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.

What is loud? Noise is a sound that disturbs or harms.
What we condemn as noise depends not only on the noise level. There are
social, physical and psychological factors. Besides the type of noise and
personal noise sensitivity there are the expectations of a person which is crucial
to its assessment of noise. The "desired" noise is not the classification in 'noisy'
or 'too loud'. Kurt Tucholsky wrote: "Our own dog does not make noise, it only
barks" and "noise is the sound of the others."
What is the highest sound pressure possible?
How many decibels is the loudest noise?

Assumption: The greatest sound pressure that cannot be exceeded because
the average air pressure is 101325 Pa. This sound pressure level is:
L = 20 × log (101 325 / 0.000 02) = 194 dB SPL.
Pay attention, RMS value is not peak value.
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 has
to be asymmetric. Even louder noise is possible, but heavily distorted. That's
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.
These madness sound levels will never be measured but only estimated or
Ultrasound between 20 kHz and 1.5 GHz does not belong to our human hearing.
Infrasound below about 16 Hz is not audible for the human ear, but we can feel
high sound levels.

The total sound power is emitted by the sound source. Sound power levels
are connected to the sound source and are independent of distance.
Sound pressure levels vary substantially with distance from the source.
 Sound pressure p in pascals (newtons per square meter) is not the
 same physical size as intensity J or I in watts per square meter.
 ... and the sound power (acoustic power) does not decrease with
 distance from the sound source - neither with 1 / r nor as 1 / r2.

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 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)
 ↔  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 (SPL air)
 ↔  Sound intensity level LI (air)
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
The sound pressure level in the air matchthe sound intensity level when we
choose a reference sound characteristic impedance of
Z0 = 400 N·s/m³.
This is not the case with the distance independent sound power level.

Source of disturbance - Musical instrument? Sound power (German)?
Sound pressure levels are not sound power levels (German)

There is no "dBA" value given as threshold of human hearing.
These values are not given as dBA, but as dBSPL, that means without any weighting filter.
Comparison of sound pressure level SPL and sound intensity level
Formula for level
Sound power level
The sound field quantity as sound pressure p acting on the tympanic membranes of
the ears is generally relevant to the subjective sensation of sound. When it comes to
our ears and hearing, it is recommended to avoid the less appropriate expressions
of the sound energy quantities such as sound power and sound intensity aside. As
sound engineers let us care while listening especially to the sound pressure, or the
sound pressure levelas sound field quantity. The architectural acoustics absolutely
needs the sound energy sizes. In this region of calculation the "artistic ears" are less
switched on. So we are just listening to the sound pressure, or the sound pressure
level SPL.
The sound pressure level decreases in the free field with 6 dB per distance doubling.
That is the 1/r law.
Often it is argued the sound pressure would decrease after the 1/r2 law
(inverse square law). That's wrong.
The sound pressure in a free field is inversely proportional to the distance from the
microphone to the source. p ~ 1/r.

How does the sound decrease with increasing distance?
Damping of sound level with distance

Relation of sound intensity, sound pressure and distance law:

From this follows    Schalldruck-Abstand
Note: The often used term "intensity of sound pressure" is not correct.
Use "magnitude", "strength", "amplitude", or "level" instead.
"Sound intensity" is sound power per unit area, while "pressure" is a
measure of force per unit area. Intensity (sound energy size) is not
equivalent to pressure (sound field size).
dB scale for field sizes, like volts and sound pressures
dB Spannungsverhältnis - sengpielaudio
The sound pressure is the force F in newtons N of a sound on a
surface area A in m2 perpendicular to the direction of the sound.
The SI-unit for the sound pressure p is N/m2 = Pa.            p ~ 1/r.

How to measure sound pressure?
Sound (pressure) level meter - SPL = Sound Pressure Level

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.

Note - Comparing dBSPL and dBA:
            There is no conversion formula for measured dBA
            values to sound pressure level dBSPL or vice versa.

            That is only possible measuring one single frequency.

There is no "dBA" curve given as threshold of human hearing.

The weighted sound level is neither a physiological nor a
physical parameter.
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.


Readings of a pure 1 kHz tone should be identical, whether weighted or not.

How loud is dangerous?
Typical dbA levels

190 dBA   Heavy weapons, 10 m behind the weapon (greatest level)
180 dBA   Toy pistol fired close to ear (greatest level)
170 dBA 

 Slap on the ear, fire cracker explodes on shoulder, small arms
 at a distance of 50 cm (greatest level)

160 dBA   Hammer stroke on brass tubing or steel plate at 1 m distance,
 airbag deployment very close at a distance of 30 cm (greatest level)
150 dBA   Hammer stroke in a smithy at 5 m distance (greatest level)
130 dBA   Loud hand clapping at 1 m distance (greatest level)
120 dBA   Whistle at 1 m distance, test run of a jet at 15 m distance
   Threshold of pain, above this fast-acting hearing damage in short action is possible
115 dBA   Take-off sound of planes at 10 m distance
110 dBA   Siren *) at 10 m distance, frequent sound level in discotheques and close
 to loudspeakers at rock concerts, violin close to the ear of an orchestra
 musicians (greatest level)
105 dBA   Chain saw at 1 m distance, banging car door at 1 m distance (greatest level),
 racing car at 40 m distance, possible level with music head phones
100 dBA   Frequent level with music via head phones, jack hammer at 10 m distance
95 dBA   Loud crying, hand circular saw at 1 m distance
90 dBA   Angle grinder outside at 1 m distance
   Over a duration of 40 hours a week hearing damage is possible
85 dBA   2-stroke chain-saw at 10 m distance, loud WC flush at 1 m distance
80 dBA   Very loud traffic noise of passing lorries at 7.5 m distance,
 high traffic on an expressway at 25 m distance
75 dBA   Passing car at 7.5 m distance, un-silenced wood shredder at 10 m distance
70 dBA   Level close to a main road by day, quiet hair dryer at 1 m distance to ear
65 dBA   Bad risk of heart circulation disease at constant impact is possible
60 dBA   Noisy lawn mower at 10 m distance
55 dBA   Low volume of radio or TV at 1 m distance, noisy vacuum cleaner at
 10 m distance
50 dBA   Refrigerator at 1 m distance, bird twitter outside at 15 m distance
45 dBA   Noise of normal living; talking, or radio in the background
40 dBA   Distraction when learning or concentration is possible
35 dBA   Very quiet room fan at low speed at 1 m distance
25 dBA   Sound of breathing at 1 m distance
0 dB     Auditory threshold
Loud noise measured in dBA with an A-weighting filter
are showing always too low measured values.
There is no formula for calculating "equal loudness"
Note - Comparing dBSPL and dBA:
            There is no conversion formula for measured dBA
            values to sound pressure level dBC or dBSPL.

            That is only possible measuring one single frequency. 
There is no "dBA" curve given as threshold of human hearing.

Also no dBC measured values can be converted to dBA values.
The frequency composition of the signal is not known.

*) A small frequency region makes high volume; see: Loudspeaker efficiency versus sensitivity
"Amateurs" frequently ask about the high dB values from a siren. They are satisfied with each
mentioned dB value. But they are not interested on the important distance from the noise source.
That shows that they are just "dummies".
How loud is a siren? The closer you get with ears to the sound source, the louder it will be.

The loved term "low volume" (Zimmerlautstärke)
Anyone who feels disturbed in his apartment from the noise of the neighbors thinks it must give a
measurable value for "low volume", which may not exceeded by the neighbor. Since volume is a
personal not measurable subjective sensation in the ears of the deranged, no decibel value for the low
room volume was determined by the courts. Noise is always the produced annoying noise of others.

There is no objective judicially accepted definition of a sound level in decibels of low volume basis.
Rated sound is not specified in phones, but increasingly in dB (A).
If in the measurement of the noise the distance to the measurement microphone is not specified,
this information is worthless. This unfortunately happens quite often.

The sound power level in dB ist not the sound pressure level (SPL) or the sound intensity level!
This information is often not understood or seems to be confusing.

From a dB-A measurement no accurate description of the expected noise volume is possible.

Table of the Threshold of pain

What is the pain threshold? The point at which pain begins to be felt.
Following rounded values are given in various audio articles and books:

Sound pressure level
    Sound pressure    
    140 dBSPL 200 Pa
   137.5 dBSPL 150 Pa
    134 dBSPL 100 Pa
    130 dBSPL   63 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.

Schallpegel und Einwirkzeit

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.
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 working lifetime.
The answer to the question whether NIOSH or OSHA have more "correct" decibel values,
may depend on the different perspective of the employer and the employee.
Noise protection always costs money.

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

Sound pressure level
94 dB + dB
 ↔  Permissible exposure time

Integration time of hearing

Integration times of hearing:
ca. 100 µs to 3 ms / 10 ms (sum localization)
ca. 5 ms to 10 ms: echo threshold / masking
ca. 10 ms coupling width
ca. 50 ms pitch detection (recognition)
ca. 250 ms sound smearing / quasi-stationary processes.

The Psychoacoustic Loudness

Note: Which increase corresponds to a doubling of the sound (factor = 2)?
An increase of the sound level by 3 dB corresponds to a doubling of sound intensity.
An increase of the sound level by 6 dB corresponds to a doubling of the sound pressure.
An increase in the sound level by 10 dB corresponds to the sensation of double the "volume".

The subjective perceived "volume" or "loudness level" and the artificial term "loudness" has not to
be mixed with the objective measure of sound pressure as sensation size of the human sense of
hearing. The sound pressure as a sound field size is not the same as the sound intensity as sound
energy size. Psychoacousticians tell us that a level increase of 10 dB should result in an impression
of doubling the loudness (volume). If we have 6 violins as the initial source, then we need 10 times
the violins, or 60 violins to double the psychoacoustic volume (loudness).
Half loudness ≡ level          −10 dB  Double loudness ≡ level                +10 dB
Half sound pressure ≡ level −6 dB  Double sound pressure ≡ level       +6 dB
Half power ≡ level                −3 dB  Double power: ≡ level                     +3 dB
four times power ≡ level       +6 dB  Ten times power ≡ level                +10 dB
Double distance ≡ level       −6 dB  Double sources (Double power) ≡  +3 dB
Note: For example, when the sound system with spaced loudspeakers delivers
twice the sound pressure as "one" amplifier,the fourfold power is required. So we
need to double the "sound pressure" for example, four parallel amplifiers of the
same design. Frequently one hears the novice question: How much more speaker
power do we need for double the "volume" (loudness)? This takes about ten
the power.

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) 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.
Subjectively perceived loudness (volume),
objectively measured
sound pressure (voltage), and
theoretically calculated
sound intensity (acoustic power)
Sound pressure
Acoustic Power
Sound Intensity
+60 dB 64 1 000   1 000 000
+50 dB 32 316   100 000
+40 dB 16 100   10 000
+30 dB   8    31.6 1 000
+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 1/4 = 0.25         0.100    0.01
−30 dB 1/8 = 0.125       0.031 6    0.001
−40 dB 1/16 = 0.062 5    0.010 0      0.000 1
−50 dB 1/32 = 0.031 2    0.003 2      0.000 01
−60 dB 1/64 = 0.015 6    0.001 0     0.000 001
Log. size Psycho size Field size Energy size
dB change Loudness multipl. Amplitude multiplier Power multiplier

The psycho-acoustic volume or loudness is a subjective sensation size.

Is a 10 dB or 6 dB sound level change for a doubling or halving of the loudness (volume) correct?
About the connection between sound level and loudness, there are various theories. Far spread is still the
theory of psycho-acoustic pioneer Stanley Smith Stevens, indicating that the doubling or halving the
sensation of loudness corresponds to a level difference of 10 dB. Recent research by Richard M. Warren,
on the other hand leads to a level difference of only 6 dB. *) This means that a double sound pressure
corresponds to a double loudness. The psychologist John G. Neuhoff found out that for the rising level our
hearing is more sensitive than for the declining level. For the same sound level difference the change of
loudness from quiet to loud is stronger than from loud to quiet.
It is suggested that the sone scale of loudness reflects the influence of known experimental biases and
hence does not represent a fundamental relation between stimulus and sensation.

*) Richard M. Warren, "Elimination of Biases in Loudness Judgments for Tones", 1970, Journal
of the Acoust. Soc. Am. Volume 48, Issue 6B, pp. 1397 - 1403
Richard M. Warren, "Quantification of Loudness", 1973, American Journal of Psychology,
Vol 86 (4), pp. 807 - 825

John G. Neuhoff, "An adaptive bias in the perception of looming auditory motion", 2001,
Ecological Psychology 13 (2) pp. 87 - 110
John G. Neuhoff, "Perceptual Bias for Rising Tones", 1998, Nature, Volume 395,
10 September

Citation: When known experimental biases were eliminated, half loudness was equal to half sound
pressure level (−6 dB) from 45 to 90 dB.

It follows that the determination of the volume (loudness) which is double as loud should not
be dogmatically defined. More realistic is the claim:
A doubling of the sensed volume (loudness) is equivalent
to a level change approximately between 6 dB and 10 dB.

Subjectively perceived loudness (volume),
objectively measured sound pressure (voltage), and
theoretically calculated sound intensity (acoustic power)

Psychoacoustic: Relationship between phon and sone
Conversion of sound units (levels)
Calculations of sound values and their levels
Conversion of voltage V to dBm, dBu, and dBV
Question: What is the standard distance to measure sound pressure level away from equipment?
There is really no standard distance for measuring dB (decibels). It depends on the size of the
sound source and the sound pressure level.
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 a sound field quantity.
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 as a sound engineer and sound
designer (ear people) you don't need that sound energy quantity.
Who is involved in audio engineering, should rather take care of the
sound field quantity, that is the sound pressure or the sound pressure
level (SPL) as an effect at the eardrums of our hearing and on the
diaphragms of the microphones, and the corresponding audio voltage
and its voltage level.


Sound pressure and Sound power − Effect and Cause

Ratio magnitudes and levels

The decibel is defined as a 20 times logarithm of a ratio of linear sizes to each other
and as a 10 times logarithm of a ratio of quadratic sizes to each other.
Ratios of electric or acoustic sizes, such as electric voltage and the sound pressure
is referred to as ratios (factors), such as reflection factor.
Ratios of square sizes to one another, such as power and energy are called grades,
such as efficiency.
Logarithmically ratios of electric or acoustic sizes of the same unit, we express as
measures such as transfer factor, or level, such as sound pressure level.
Levels are measured in decibels - dB in short.
If the output voltage level is 0 dB, that is 100%, the level of −3 dB
is equivalent to 70.7% and the level of
−6 dB is equivalent to 50%
of the initial output voltage.
This applies to all field sizes; e.g. sound pressure.
If the output power level is 0 dB, that is 100%, the level of
−3 dB
is equivalent to 50%
and the level of −6 dB is equivalent to 25%
of the initial output power.
This applies to all energy sizes; e.g. sound intensity.
Try to understand this.


Conversion of sound pressure to sound power and vice versa

The sound pressure changes depending on the environment and the
distance from the sound source. In contrast, the sound power of a sound
source is location-independent.
Formulas for conversion:
Acoustical power (sound power)
Pac = I × Ain watts
Sound intensity I = peff2 / Z0 in W/m2 = Pac / Ain W/m2
Perfused area A = 4 × π × r2 in m2
Distance measurement point from the sound source r in meters (has only
meaning with sound pressure, not with sound power)
Acoustic impedance of air Z0 = 413 N·s/m3 at 20 C
Sound pressure peff in Pa = N/m2
In point-like sound sources spherical areas A shall be inserted.
Depending on the arrangement following sections are taken into account:
Solid sphere - sound source anywhere in the room, Q = 1
Hemisphere - sound source on the ground, Q = 2
Quarter Sphere - sound source on the wall, Q = 4
Eighth sphere - sound source in the corner, Q = 8
Q = direction factor and area A = (4 × π × r2) / Q

Compare Sound power level and sound pressure level
in a distance from the sound source

A typical question: "What is the dB volume of a symphony orchestra?"
Answer: "It really depends on the distance from the listener to the orchestra."
To name the distance is often "forgotten". They want to hear only a decibel
number. But only a dB number is really senseless.
There is a constant uncertainty of the answer to the question:
"How many decibels (dB) are doubling a sound"? or "What is twice the sound?"

Answer: Doubling means the "factor 2". What does doubling of a "sound" mean?
Doubling the (sound) intensity is obtained by an increase of the sound intensity level of 3 dB.
Doubling the sound pressure is obtained by an increase of the sound pressure level of 6 dB ●
Doubling the loudness feeling is obtained by an increase of the loudness level of about 10 dB. 

Double or twice the power = factor 2 means 3 dB more calculated power level (sound intensity level).
Double or twice the voltage = factor 2 means 6 dB more measured voltage level (sound pressure level)
Double or twice the loudness = factor 2 means 10 dB more sensed loudness level (psycho acoustic)
Simple rule of thumb:
When working with power, 3 dB means double (twice) the factor and 10 dB means 10-fold. When
working with voltage or current, 6 dB means double (twice) the factor and 20 dB means 10-fold.
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
In sound engineering there is no power matching or impedance matching.
In audio we use only
voltage bridging or high impedance bridging.
Please read the following information carefully:
8 Ohm Output" and "150 Ohm Input" − What is that?

Thresholds of hearing and perception and - Frequency region of infrasound
Theshold Sound pressure level (SPL) at a frequency of
Frequency 8 Hz 10 Hz 12,5 Hz 16 Hz 20 Hz
Auditory threshold of hearing 103 dB 95 dB 87 dB 79 dB 71 dB
Auditory threshold of perception 100 dB 92 dB 84 dB 76 dB 68 dB
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