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Sound pressure
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Sound pressure is the local pressure deviation from the ambient (average, or equilibrium) pressure caused by a sound wave. Sound pressure can be measured using a microphone in air and a hydrophone in water. The SI unit for sound pressure is the pascal (symbol: Pa). The instantaneous sound pressure is the deviation from the local ambient pressure p0 caused by a sound wave at a given location and given instant in time. The effective sound pressure is the root mean square of the instantaneous sound pressure over a given interval of time (or space). In a sound wave, the complementary variable to sound pressure is the acoustic particle velocity. For small amplitudes, sound pressure and particle velocity are linearly related and their ratio is the acoustic impedance. The acoustic impedance depends on both the characteristics of the wave and the medium. The local instantaneous sound intensity is the product of the sound pressure and the acoustic particle velocity and is, therefore, a vector quantity.
The sound pressure deviation p is
where
- F = force,
- A = area.
The entire pressure ptotal is
where
- p0 = local ambient pressure,
- p = sound pressure deviation.
Examples of sound pressure and sound pressure levels Sound pressure in air:
| Source of sound | Sound pressure | Sound pressure level |
|---|
| | pascal | dB re 20 µPa |
|---|
Theoretical limit for undistorted sound at
1 atmosphere environmental pressure | 101,325 Pa | 191 dB | | Krakatoa explosion at 100 miles (160 km) in air | 20,000 Pa | 180 dB | | Simple open-ended thermoacoustic device | 12,000 Pa | 176 dB | | M1 Garand being fired at 1 m | 5,000 Pa | 168 dB | | Jet engine at 30 m | 630 Pa | 150 dB | | Rifle being fired at 1 m | 200 Pa | 140 dB | | Threshold of pain | 100 Pa | 130 dB | | | 126 dB | | Hearing damage (due to short-term exposure) | 20 Pa | approx. 120 dB | | Jet at 100 m | 6 – 200 Pa | 110 – 140 dB | | Jack hammer at 1 m | 2 Pa | approx. 100 dB | | Hearing damage (due to long-term exposure) | 6×10-1 Pa | approx. 85 dB | | Major road at 10 m | 2×10-1 – 6×10-1 Pa | 80 – 90 dB | | Passenger car at 10 m | 2×10-2 – 2×10-1 Pa | 60 – 80 dB | | TV (set at home level) at 1 m | 2×10-2 Pa | approx. 60 dB | | Normal talking at 1 m | 2×10-3 – 2×10-2 Pa | 40 – 60 dB | | Very calm room | 2×10-4 – 6×10-4 Pa | 20 – 30 dB | | Leaves rustling, calm breathing | 6×10-5 Pa | 10 dB | | Auditory threshold at 2 kHz | 2×10-5 Pa | 0 dB |
Sound pressure in water:
| Source of sound | Sound pressure | Sound pressure level |
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| | pascal | dB re 1 µPa |
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| Auditory threshold of a diver at 1 kHz | 2.2 · 10-3 Pa | 67 dB |
The formula for the sum of the sound pressure levels of n incoherent radiating sources is
From the formula of the sound pressure level we find
This inserted in the formula for the sound pressure level to calculate the sum level shows
Beyond 191 dBAs sound pressure levels approach 191 dB in air at sea level, their waveforms become distorted; the exact level at which this happens varies with the barometric pressure. Sound waves are made up of rarefaction and compression cycles, but when the compression half of the wave cycle is double atmospheric pressure, the rarefaction half of the cycle approaches a perfect vacuum (no further air molecules to remove). At this point, the only possible increase in sound level that could be achieved is on the compression side of the waveform. (The rarefaction half of a sine wave would be clipped at any level above about 191 dB.) Any wave approaching these intensities is no longer considered sound, but a shock wave. Examples of such an occurrence are large-scale manned rocket launches, sonic booms, munitions explosions, thunder, earthquakes and volcanic explosions.
See also
External links
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