Livelli di pressione sonora en
From "Physics, Waves, Music": a website about the physics of waves and sound, acoustics of musical instruments, musical scales, harmony and music.
| AI-translated from Italian. Original page: Livelli_di_pressione_sonora |
The sound pressure level (SPL) is the measure in dB of the deviation from the ambient air pressure caused by a sound wave.
A sound wave produces pressure variations that change from place to place and from instant to instant. For this reason, reference is more often made to the effective pressure, that is, the root mean square deviation of the pressure over a certain time interval.
Remember, however, that the pressure variations caused even by the loudest sound that can be tolerated are a thousand times smaller than the value of atmospheric pressure at sea level. Sound pressure variations are therefore to be regarded as small "ripples" on the value of atmospheric pressure.
The sound pressure level is defined as
where p is the root mean square deviation of the pressure, and p0 is a reference value for the sound pressure, which in air takes the standard value of 20 µPa.
| Sound source | Sound pressure | Sound pressure level |
|---|---|---|
| Pa | dB(SPL) | |
| Threshold of pain | 100 | 134 |
| Hearing damage from short exposure | 20 | ca. 120 |
| Jet at 100 m | 6 - 200 | 110 - 140 |
| Jackhammer at 1 m / Disco | 2 | ca. 100 |
| Hearing damage from long exposure | 6×10−1 | ca. 90 |
| busy road at 10 m | 2×10−1 - 6×10−1 | 80 - 90 |
| car at 10 m | 2×10−2 - 2×10−1 | 60 - 80 |
| TV at 1 m | 2×10−2 | ca. 60 |
| Speech at 1 m | 2×10−3 - 2×10−2 | 40 - 60 |
| Very quiet room | 2×10−4 - 6×10−4 | 20 - 30 |
| Breathing | 6×10−5 | 10 |
| Threshold of hearing at 2 kHz | 2×10−5 | 0 |
- For a conversion table between the many units of pressure, see pressure and its units.
- For a discussion of the logarithmic scale used to measure sound intensity, see also Perception of loudness
- For the properties of the logarithm function, see The logarithm function
Check your understanding
Problem. A sound level meter measures an effective pressure of 2 Pa. What is the sound pressure level? And if the effective pressure is 1 Pa, like that produced by sound level meter calibrators?
Solution. 2 Pa: 20 log10(2/(2·10−5)) dB = 20 log10(105) dB = 100 dB. 1 Pa: 20 log10(5·104) dB ≈ 94 dB. Halving the pressure lowers the level by about 6 dB.Problem. Two identical, independent sources each produce 70 dB at a certain point. What is the level when they play together?
Solution. For independent (incoherent) sources the squares of the effective pressures, that is the intensities, add: the square doubles and the level increases by 10 log102 dB ≈ 3 dB, becoming about 73 dB, not 140 dB. Only if the two waves were exactly in phase would the pressures add, with an increase of 6 dB.Problem. By how much does the sound pressure level increase if the effective pressure becomes 10 times larger? And if it becomes 1000 times larger?
Solution. 20 log1010 dB = 20 dB and 20 log101000 dB = 60 dB. In the table, from the TV at 1 m (60 dB) to the threshold of pain (134 dB) the pressure increases 5000 times.Further reading and links
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