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Domain of Psychoacoustics
| The subjective perceived sound volume and the artificial term loudness. The volume or loudness of a noise is given in sone. 1 sone is equivalent to 40 phons, which is 40 dBSPL of a sine wave of 1000 Hz. |
Conversion valid between 40 phons and 120 phons
For loudness level LN > 40 phons: loudness N in sones = 2[(LN in phons − 40)/10]
For loudness N > 1 sone: loudness level LN in phons = 40 + [10 × log N / log102] in sones
log 2 = 0.301029995
Conversion only valid between 8 phons and 40 phons
For loudness level LN < 40 phons: loudness N in sones = (LN in phons / 40)2.86 − 0.005
For loudness N < 1 sone: loudness level LN in phons = 40 × (N in sones + 0.0005)0,35
| According to Stanley Smith Stevens' definition, 1 sone is equivalent to 40 phons, which is defined as the loudness level of a pure 1 kHz tone at LN = 40 dBSPL, or dBA, but only (!) for a sine wave of 1 kHz and not for broadband noise. There is no "dBA" curve given as threshold of human hearing. |
Relation between loudness N in sones
and loudness level LN in phons
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Loudness N (sone) and loudness level LN (phon), as shown here, is easily converted into one another. But the psychoacoustic perceived loudness level and the objectively measured sound pressure level in dBSPL cannot be converted to the weighted dBA level. There is no formula. The typical question: "How to convert 0.5 sone to decibel (dB)?" cannot be answered. Only a pure tone of 1 kHz measured in phons is equivalent to a dB-SPL value. |
| The volume of a sound is a subjective perception. To "measure" loudness, the volume of a 1,000 hertz reference tone is adjusted until it is perceived by listeners to be equally as loud as the sound being "measured". The loudness level, in phons, of the sound is then equal to the sound-pressure level, in decibels. Readings of a pure 1 kHz tone should be identical, whether weighted or not. Between the loudness N in sone and the loudness level LN in phon we have the following connection (ISO-recommendation ISO/R 131-1959): Loudness N = 2(LN − 40)/10 or loudness level LN = 40 + 10 × lb N. "lb" means logarithm base 2. 10 × lb N = 10 × log2(N) The sone is a unit of perceived loudness after a proposal of Stanley Smith Stevens (1906-1973) in 1936. In acoustics, loudness is a subjective measure of the sound pressure. One sone is equivalent to 40 phons, which is defined as the loudness of a 1 kHz tone at 40 dBSPL. 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 (= √10). At frequencies other than 1 kHz, the measurement in sones must be calibrated according to the frequency response of human hearing, which is of course a subjective process. The study of apparent loudness is included in the topic of psycho acoustics. Volume in acoustics is used as a synonym for loudness. It is a common term for the amplitude or the level of sound. To be fully precise, a measurement in sones must be qualified by the optional suffix G, which means that the loudness value is calculated from frequency groups, and by one of the two suffixes F (for free field) or D (for diffuse field).
With the following table you can try to convert roughly, but be cautious using these psychoacoustic values. The frequency composition of the signal amplitude is always unknown. The distance of the measuring point is important for the value of the measure. The following chart is, however, for the dBA values no accurate knowledge − it's more a guess. "Conversion" of "sone to dBA" |
Conversion between sones and phons,
but more of a guess for dBA
| sones | phons | dBA | sones | phons | dBA | |
| 0.1 | 17.9 | 20.5 | 1.8 | 48.5 | 34.8 | |
| 0.2 | 22.8 | 21.5 | 1.9 | 49.3 | 35.3 | |
| 0.3 | 26.2 | 22.5 | 2.0 | 50.0 | 35.8 | |
| 0.4 | 29.0 | 23.5 | 2.1 | 50.7 | 36.4 | |
| 0.5 | 31.4 | 24.4 | 2.2 | 51.4 | 37.0 | |
| 0.6 | 33.5 | 25.3 | 2.3 | 52.0 | 37.5 | |
| 0.7 | 35.3 | 26.3 | 2.4 | 52.6 | 38.0 | |
| 0.8 | 37.0 | 27.2 | 2.5 | 53.2 | 38.4 | |
| 0.9 | 38.6 | 28.2 | 2.6 | 53.8 | 38.8 | |
| 1.0 | 40.0 | 29.2 | 2.7 | 54.3 | 39.3 | |
| 1.1 | 41.4 | 30.2 | 2.8 | 54.9 | 39.8 | |
| 1.2 | 42.6 | 31.1 | 2.9 | 55.4 | 40.2 | |
| 1.3 | 43.8 | 32.0 | 3.0 | 55.9 | 40.6 | |
| 1.4 | 44.9 | 33.0 | 3.1 | 56.3 | 41.1 | |
| 1.5 | 45.9 | 33.5 | 3.2 | 56.8 | 41.5 | |
| 1.6 | 46.9 | 33.9 | 3.3 | 57.2 | 42.0 | |
| 1.7 | 47.7 | 34.4 | 3.4 | 57.7 | 42.5 |
| Words to the wise: 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
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| This frequency weighting with the A-curve is used for noise measurements. It is close to the frequency response of the human hearing for levels below 30 dB only. But the filter is also used for higher levels, and therefore gives lower values as our ears are feeling. The cut off low frequencies are not measured. |
| A formula with a cautious try to convert sones to decibels: dBA = 33.22 × log (sones) + 28 with a possible accuracy of ± 2 dBA or sones = 10^[(dBA − 28) / 33.22] |
| The phon is a unit of perceived loudness level, which is a subjective measure of the strength (not intensity) of a sound. At a frequency of 1 kHz, 1 phon is defined to be equal to 1 dB of sound pressure level above the nominal threshold of hearing, the sound pressure level SPL of 20 µPa (micropascals) = 2×10−5 pascal (Pa). Our ears as sensors cannot convert sound intensities and powers, they can only use the sound pressure changes between 20 Hz and 20,000 Hz. At other frequencies, the phon departs from the decibel, but is related to it by a frequency weighting curve (equal-loudness contour) that reflects the frequency response of human hearing. The standard curve for human hearing is the A-weighted curve (the equal-loudness contour for a 40 dB stimulus at 1 kHz), but others are in use.
The "unit" phon has been largely replaced by the dBA (A-weighted decibel), though many old textbooks and instructors continue to use the phon. Note: "Set the volume of the radio double as loud or half as loud." Who does not know, how to do this, is a normal person. Psycho-acousticians are telling us, that it has to be 10 dB level difference. Try to cool your hot coffee to the point "half as hot" - and think it over. Your own feeling may be much different to other persons. An increase from 6 dB to 10 dB is perceived by most listeners as "double" the volume. These sensations are highly subjective, meaning that different people will hear this in different ways, and "twice as loud" is a much harder thing to guess than something. 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. |
Sound Level Comparison Chart with 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 |
| 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 factor 3.16. Loudness and volume are highly subjective. That belongs to the domain of psychoacoustics. |
| 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 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. |
| How do you convert sound quantities to decibel values? How many decibels is twice (double, half) or three times as loud? How does the sound decrease with distance? |
Weighting filter after DIN EN 61672-1 2003-10 (DIN-IEC 651) - weighted dB-A and dB-C
A program to combine as much as ten (10) noise sources
Conversion of sound pressure level to sound pressure and sound intensity
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