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| To get a feeling for decibels, look at the table below which gives values for the
sound pressure levels of common sounds in our environment. Also shown are the corresponding sound pressures and sound intensities. From these you can see that the decibel scale gives numbers in a much more manageable range. Sound pressure levels are measured without weighting filters. The values are averaged and can differ about ±10 dB. With sound pressure is always meant the effective value (RMS) of the sound pressure, without extra announcement. The amplitude of the sound pressure means the peak value. The ear is a sound pressure receptor, or a sound pressure sensor, i.e. the ear- drums are moved by the sound pressure, a sound field quantity. It is not an energy receiver. When listening, forget the sound intensity as energy quantity. The perceived sound consists of periodic pressure fluctuations around a stationary mean (equal atmospheric pressure). This is the change of sound pressure, which is measured in pascal (Pa) ≡ 1 N/m2 ≡ 1 J / m3 ≡ 1 kg / (m·s2). Usually p is the RMS value. |
| Table of sound levels L (loudness) and corresponding sound pressure and sound intensity |
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| Sound Sources (Noise) Examples with distance |
Sound Pressure Level Lp dB SPL |
Sound Pressure p N/m2 = Pa sound field quantity |
Sound Intensity I W/m2 sound energy quantity |
|
| Jet aircraft, 50 m away | 140 | 200 | 100 | |
| Threshold of pain | 130 | 63.2 | 10 | |
| Threshold of discomfort | 120 | 20 | 1 | |
| Chainsaw, 1 m distance | 110 | 6.3 | 0.1 | |
| Disco, 1 m from speaker | 100 | 2 | 0.01 | |
| Diesel truck, 10 m away | 90 | 0.63 | 0.001 | |
| Kerbside of busy road, 5 m | 80 | 0.2 | 0.0001 | |
| Vacuum cleaner, distance 1 m | 70 | 0.063 | 0.00001 | |
| Conversational speech, 1 m | 60 | 0.02 | 0.000001 | |
| Average home | 50 | 0.0063 | 0.0000001 | |
| Quiet library | 40 | 0.002 | 0.00000001 | |
| Quiet bedroom at night | 30 | 0.00063 | 0.000000001 | |
Background in TV studio |
20 | 0.0002 | 0.0000000001 | |
| Rustling leaves in the distance | 10 | 0.000063 | 0.00000000001 | |
| Threshold of hearing | 0 | 0.00002 | 0.000000000001 | |
| 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 source is really meaningless. Unfortunately this error (unknown distance) is quite often to find. |
| Noise is a sound that disturbs or harms. |
Assumption: The maximum sound pressure is 194 dBSPL that cannot be
exceeded because the average air pressure of 101325 Pa. |
| 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 quantity as intensity J or I in watts per square meter. ... and the sound power (acoustic power) does not decrease with distance r from the sound source - neither with 1 / r nor as 1 / r2. |
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 |
| The reference sound pressure level for 0 dBSPL is the sound pressure
p0 =
20 µPa = 20 × 10−6 Pa = 2 × 10−5 Pa = 0.00002 Pa or N/m². That is the
threshold of hearing. (The reference sound intensity is I0 = 10−12 W/m2.) Pa = Pascal. 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. 
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Differentiate between sound pressure p as a "sound field quantity" and sound
intensity I as a "sound energy quantity". I ~ p2 for progressive plane waves. When it comes to our ears and the hearing, it is recommended that the inappropriate expression of the sound energy parameters, such as sound power (acoustic power) and sound intensity to leave aside. So we are just listening to the sound pressure as sound field quantity, 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:
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| 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 quantity) is not equivalent to pressure (sound field quantity). |
| dB scale for field quantities, like volts and sound pressures |
 |
| ratio |
| 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. |
| 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. *) |
*) http://www.google.com/search?q=Always+wonder+what+a+manufacturer+Rane&filter=0
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 (maximum level) |
| 180 dBA | Toy pistol fired close to ear (maximum level) |
| 170 dBA | Slap on the ear, fire cracker explodes on shoulder, small arms |
| 160 dBA | Hammer stroke on brass tubing or steel plate at 1 m distance, airbag deployment very close at a distance of 30 cm (maximum level) |
| 150 dBA | Hammer stroke in a smithy at 5 m distance (maximum level) |
| 130 dBA | Loud hand clapping at 1 m distance (maximum 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 (maximum level) |
| 105 dBA | Chain saw at 1 m distance, banging car door at 1 m distance (maximum 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 dBA | Auditory threshold |
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?
You can find the following rounded values in various audio articles and books:
| Sound pressure level Lp |
Sound pressure p |
| 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. |
How long can a person listen to noise of a certain sound level before hearing damage occurs? |
| Sound Pressure Level | Permissible Exposure Time |
| 115 dB | 0.46875 minutes (~30 sec) |
| 112 dB | 0.9375 minutes (~1 min) |
| 109 dB | 1.875 minutes (< 2 min) |
| 106 dB | 3.75 minutes (< 4 min) |
| 103 dB | 7.5 minutes |
| 100 dB | 15 minutes |
| 97 dB | 30 minutes |
| 94 dB | 1 hour |
| 91 dB | 2 hours |
| 88 dB | 4 hours |
| 85 dB | 8 hours |
| 82 dB | 16 hours |
| Accepted standards for recommended permissible exposure time for continuous time weighted average noise, according to NIOSH and CDC, 2002. For every 3 dBs over 85 dB, the permissible exposure time before possible damage can occur is cut in half. |
The Psychoacoustic Loudness
| Note: Which increase corresponds to a doubling of the sound? An increase of the sound level by 3 dB corresponds to a doubling (factor = 2) 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 mixedwith the objective measure of sound pressure as sensation size of the human sense of hearing. The sound pressure as a sound field quantity is not the same as the sound intensity as sound energy quantity. Psychoacousticians tell us that a level increase of 10 dB should result in an impression of doubling the loudness (volume). If you have 6 violins as the initial source, then you 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 |
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) |
| 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 |
The psycho-acoustic volume or loudness is a subjective sensation size.
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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" 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. |
| Conversion of sound units (levels) Calculations of Sound Values and their Levels Conversion of voltage V to dBm, dBu, and dBV |
| The total sound power is emitted from the sound source. The sound power level and the sound power is connected firmly with the sound source and is really independent of the distance. On the other hand, the SPL varies significantly with the distance from the sound source. |
| 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. |
| Sound pressure p in pascals is not the same physical quantity as intensity I in watts per square meter. ... and the sound power (acoustic power) does not decrease with distance r from the sound source - neither with 1 / r nor as 1 / r2. |
| Often the sound pressure as a sound field quantity is mixed incorrectly with the sound intensity as a sound energy quantity. But I ~ p2. |
| Note: The radiated sound power (sound intensity) is the cause - and the sound pressure is the effect. The effect is of particular interest to the sound engineer. The effect of temperature and sound pressure. |
| Acousticians and sound protectors (noise fighters) need the sound intensity (acoustic intensity). As a sound designer you don't need that. Look out more for the sound pressure that makes an effect to your ears and to the microphones. |
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 quantities to each
other and as a 10 times logarithm of a ratio of quadratic quantities to each other. Ratios of electric or acoustic quantities, such as electric voltage and the sound pressure is referred to as ratios (factors), such as reflection factor. Ratios of square quantities to one another, such as power and energy are called grades, such as efficiency. Logarithmically ratios of electric or acoustic quantities 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 quantities; 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 −6 dB is equivalent to 25% of the initial output power. This applies to all energy quantities; 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 × A in watts Sound intensity I = peff2 / Z0 in W/m2 = Pak / A in 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 of 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. |
| The constant insecurity is the answer to the question: "How many dBs are doubling a sound"? Answer: Doubling means the "factor 2". What does doubling of a "sound" mean? Twice the (sound) intensity is obtained by an increase of the (sound intensity) level of 3 dB. Twice the sound pressure is obtained by an increase of the (sound pressure) level of 6 dB. Twice the loudness feeling is obtained by an increase of the (loudness) level of about 10 dB. |
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