Sound level change and the change factor sound levels volume loudness formula calculate power level noise sound pressure intensity power relationship logarithm loudness volume decibel dB twice as loud 10 dB double distance half level dependence audio auditory hearing listening sound noise fold 3 dB 6 dB 10 dB loudness of sound SPL increase decrease - sengpielaudio
 
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Poll: Is 3 dB, 6 dB or 10 dB SPL double the sound pressure?
 
This is not a trick question. This is not about the subjective perceived loudness of hearing
and not how to add sound sources. SPL is the abbreviation for "Sound Pressure Level".
The term loudspeaker and amplification is not significantly raised with the previous survey.
It's all about sound pressure.
There is only one correct answer: Double the sound pressure is a SPL of +6 dB.
You should go on reading, if you want to know more and want to understand this.
 
Sound (music) and noise (bang)
 
Subjectively perceived loudness (volume),
objectively measured sound pressure (voltage), and
theoretically calculated sound intensity (acoustic power)
 
Dependence of sound levels and the corresponding factors
 
Often it's not about music, but about noise and noise level
 
It is not easy to understand the relationship between these terms:
There is the subjectively and artificially perceived concept of loudness,
the objectivly measurable audio voltage from a microphone which is
proportional to the sound pressure and there is the calculated sound
intensity or acoustic power.
How many decibels (dB) is twice (double, half) or three times as loud?
Loudness/Volume − What is the dependence of the level in decibels?
Does the usual word "sound level " mean the volume level, the loudness level, the sound pressure level,
thus proportional to the voltage level, the sound intensity level, the sound power level or even the A-weighted
or C-weighted sound level?
 
It is often necessary to estimate how much a sound level changes. Our ears interpret a
wide range of sound amplitude, volume or loudness as changes in level and changes in
loudness. The decibel is a very convenient unit for measuring signal levels in electronic
circuits or sound pressure levels in air. However, changes in the loudness of sounds as
perceived by our ears do not conform exactly to corresponding changes in sound
pressure level. Loudness is the quality of a sound that is the primary psychological
correlate of physical strength (amplitude). Loudness, a subjective feeling, is often
confused with objective measures of sound pressure level SPL such as decibels.
 
Definitions:
Sound level or noise level − a physical quantity measured with instruments.
Loudness − a psycho-physical sensation perceived by the human auditory
perception or the human ear/brain mechanism.
10 dB more level means double loudness are told us by the psychoacousticians.
Decibel − one-tenth of a bel, which is the logarithm of the ratio of any two energy-like
quantities or field-like quantities.

Decibel levels and perceived volume change
People feel and judge sound events after: exposure duration, spectral composition,
temporal structure, sound level, information content, and subjective mental attitude.

Sound level change and the loudness factor

To use the calculator, simply enter a value. Then use the TAB key
or click the mouse in an empty area of the page to update the result.
Calculator works in both directions of the ↔ sign.

Level change Lloud (psychoacoustics):
dB		  ↔  Factor for loudness (volume):
 fold
 
Level change Lp (field quantity):
dB		  ↔  Factor for sound pressure (voltage):
 fold
 
Level change LI (energy quantity):
dB		  ↔  Factor for acoustic intensity (power):
 fold
The factor is in mathematics part of a product. A factor is the x-fold increase of a basic quantity.
Loudness or volume is not the same as intensity. Aha, that is a light bulb moment.
The sound wave's amplitude is the change in sound pressure as the wave passes by.

Factor for loudness (volume):
 fold		  ↔  Level change Lloud (psychoacoustics):
dB
 
Factor for sound pressure (voltage):
 fold		  ↔  Level change Lp (field quantity):
dB
 
Factor for acoustic intensity (power):
 fold		  ↔  Level change LI (energy quantity):
dB
"Loudness" cannot be the same as "intensity" and
"sound intensity" is not the same as "sound pressure".
Distinguish clearly loudness, sound pressure and
(sound) intensity.

20 dB gain modification should give the factor of 4 (fourfold) for sensed volume and loudness,
20 dB gain modification gives the factor of 10 for measured voltage and sound pressure and
20 dB gain modification gives the factor of 100 for calculated sound power and acoustic intensity.
 
Doubling of the volume (loudness) should be felt by a level difference of 10 dB − acousticians say.
Doubling the sound pressure (voltage) corresponds to a measured level change of 6 dB.
Doubling of acoustic power (sound intensity) corresponds to a level change of 3 dB.
 
  3 dB = twice the power (Power respectively intensity - mostly calculated)
  6 dB = twice the amplitude (Voltage respectively sound pressure - mostly measured)
10 dB = twice the perceived volume or twice as loud (Loudness nearly sensed - psychoacoustics)
 
Instead of decibel dB you can take also dBSPL or dBA; but a level change is always in decibels dB.
The sensed volume or the loudness of a sound depends on several factors: the amplitude, that
means the sound pressure level, the frequency, and the time behavior of the sound.
A typical question on the Internet: "Are 3 dBs or 6 dBs double the loudness (or twice as loud)?"
Answer: "It's neither 3 dB nor 6 dB - it's more close to 10 dB!"

Sound Level Comparison Chart and the Factor

Table of sound level dependence and the change of the respective factor 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 (twofold)? Here are all the different factors.
Factor 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 fold  2.0 = double        4.0
  +3 dB   1.23 fold 1.414 fold = √2  2.0 = double  
  - - - - ±0 dB - - - - - - - - 1.0 - - - - - - -  - - - - 1.0 - - - - - - -  - - - - 1.0 - - - - -
  −3 dB     0.816 fold     0.707 fold    0.5 = half
  −6 dB     0.660 fold    0.5 = half 0.25
−10 dB    0.5 = half 0.316 0.01
−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
 
Factor Change in Sound
Loudness Level

Change in Sound
Pressure Level

 Change in Sound
Power Level
20 43.22 dB 26.02 dB 13.01 dB
15 39.07 dB 23.52 dB 11.76 dB
10 33.22 dB 20 dB     10 dB    
  5 23.22 dB 13.98 dB   6.99 dB
  4 20 dB     12.04 dB   6.02 dB
  3 15.58 dB   9.54 dB   4.77 dB
  2 10 dB      6.02 dB   3.01 dB
  1 0 dB    0 dB    0 dB  
1/2 = 0.5 −10 dB        −6.02 dB  −3,01 dB
     1/3 = 0.3333 −15.58 dB   −9.54 dB  −4.77 dB
  1/4 = 0.25 −20 dB       −12.04 dB    −6.02 dB
1/5 = 0.2 −23.22 dB   −13.98 dB    −6.99 dB
1/10 = 0.1   −33.22 dB   −20 dB        −10 dB     
   1/15 = 0.0667 −39.07 dB   −23.52 dB    −11.76 dB 
1/20 = 0.05  −43.22 dB   −26.02 dB    −13.01 dB 
 
The loudness factor 3 (threefold loudness) changes the sound loudness level by 15.58 dB.
The sound pressure factor 3 (threefold pressure) changes the sound pressure level by 9.54 dB.
The sound power factor 3 (threefold intensity) changes the sound power level by 4.77 dB.
 
The loudness factor 2 (twofold loudness) changes the sound loudness level by 10 dB.
The sound pressure factor 2 (twofold pressure) changes the sound pressure level by 6.02 dB.
The sound power factor 2 (twofold intensity) changes the sound power level by 3.01 dB.
 
Loudness is a subjective feeling that is often confused with objective SPL measurements in
decibels. With sound level we usually mean a logarithmic ratio of measurable sound pressures.
The number of sones to a phon was chosen so that a doubling of the number of sones sounds to
the human ear like a doubling of the loudness, which also corresponds to increasing the sound
pressure level by (+)10 dB, or increasing the sound pressure by a factor 3.16 = root of 10.

Sound loudness − Sound pressure − Sound intensity
and their levels in decibels (dB).
Different wines. The wine in the middle tastes best.
"Loudness" should never be mixed or set equal to "intensity".

Loudness - Sound pressure - Intensity

Realm of Psychoacoustic - Relationship between phon and sone
Conversion of sound units (levels)
Total Level Calculation (Adding of levels)

The often unknown formulas for level and factor.
Loudness formula - pressure formula - intensity formula

Psychoacoustics −
Level change loudnessFormula loudness level
      Factor loudness
Faktor loudness
 
Field quantity −
Level change sound pressure
Sound pressure level		      Factor sound pressure
Sound pressure factor
 
Energy quantity −
Level change sound intensity
Formel5		      Factor sound intensity
Formel6

log to the base 10 = log10 is named lg and log to the base 2 = log2 is named ld.

A typical question: How many decibels more is the 3-fold subjective loudness?
Some people have problems with the idea of "twice as loud", or "three times as loud."
I come out − I am one of them. The solution of the top calculator shows 15.85 dB. Hm ...
 
The psychoacoustic values of volume (loudness) are always signal, pulse and frequency-dependent.
Therefore a statement about this felt sensation size must be seen with a certain caution.

The work of most acoustical consultants belongs to noise control.
We speak of the volume of sound in phon or loudness in sone.
The perception of loudness is not proportional to the sound
pressure or the sound intensity. The hearing has not the same
sensitivity for all pitches.
The defined sound level is therefore not the perceived loudness of
a sound. A rough approximation to human auditory perception we
get by the use of an A-weighted filter, which approximates the sound
signal in the different frequency areas according to the sensitivity
of the hearing mechanism, but only at low levels. For louder signals
than 40 dB, this A-weighted filter cuts off incorrectly too many
low frequencies. The marketing department like this.
Note: The concept of doubling or halving a loudness, is quite vague.
Who really knows exactly when a sound is half as loud?
This corresponds to theimpossible exact rating when is a cup
of coffee half as hot? Therefore, this theoretical assumption should
not be taken too seriously.
This evaluation belongs to psychoacoustics.
Aha!

     Car Freaks und "dB Drag Racing" Fans need for their loudspeakers:
Red Power Dot The Big Power Formulas
        Electrical and mechanical power calculation 

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

Is 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"
 
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.
 

Level dynamics and spectral dynamics (timbre dynamics)

Equally important as the level dynamics, is the timbre dynamics, also called spectral dynamics.
The perceived volume (loudness) is almost independently characterized by amplitude level
through a specific timbre spectrum range played bymusical instruments as dynamic stages.

A weighting filter is used to emphasise or suppress some aspects of a phenomenon compared to others,
for measurement or other purposes. In the measurement of loudness, for example, an A-weighting filter is
commonly used to emphasize frequencies around 3 to 6 kHz where the human ear is most sensitive, while
attenuating very high and very low frequencies to which the ear is insensitive. The aim is to ensure that
measured loudness corresponds well with subjectively perceived loudness. A-weighting is only really valid
for relatively quiet sounds and for pure tones as it is based on the 40-phon equal-loudness contour; see
the weighting filtered levels dBA and dBC.
 
Another difficult issue is:
How does the volume (loudness) decrease with distance from a sound source?
How does the sound pressure (voltage) decrease with distance from a sound source?
How does the sound intensity (not the sound power) decrease with distance from a sound source?
The beginners question is quite simple: How does the sound decrease with distance?

Regenbogenlinie

Adding equal loud sound sources

Schallquellen
Level increase Δ L for
n equal loud sound sources
Number of n equal loud sound sources

Level increase
Δ L in dB
1 0
2 3.0
3 4.8
4 6.0
5 7.0
6 7.8
7 8.5
8 9.0
9 9.5
10 10.0
12 10.8
16 12.0
20 13.0

Formulas: Δ L = 10 × log n  or  n = 10Δ L / 10
Δ L = level difference; n = number of equal loud sound sources.

n = 2 equally loud incoherent sound sources result in a higher level of
10 × log10 2 = +3.01 dB compared to the case that only one source is available.
n = 4 equally loud incoherent sound sources result in a higher level of
10 × log10 4 = +6.02 dB compared to the case that only one source is available.

Calculator: Adding level of equal loud sound sources

To use the calculator, simply enter a value. Then use the TAB key or
click the mouse in an empty area of the page to update the result.
Calculator works in both directions of the ↔ sign.

 
Number of sound sources n:
 		  ↔  Increase of level Δ L:
dB
Formula1  Formula2
 

The total level in dB is the level of one sound source plus the increase of level in dB.

The decrease of sound with distance

For a spherical wave we get:
The sound pressure level (SPL) decreases with doubling of distance by (−)6 dB.
It falls to the 1/2 fold (50%) of the initial value of the sound pressure.
The sound pressure decreases with the ratio 1/r to the distance.
 
The sound intensity level decreases with doubling of distance also by (−)6 dB.
It falls to the 1/4 fold (25%) of the initial value of the acousticor sound intensity.
The sound intensity decreases with the ratio 1/r2 to the distance.
 
The loudness level decreases with doubling of distance also by (−)6 dB.
It falls to the 0.66 fold (66%) of the initial value of the sensed loudness.
The loudness decreases with the ratio 1/(20.6r) = 1/1.516 r to the distance.

Sound pressure and Sound power – Effect and Cause

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