Sound Pressure

The Sound Pressure is the force of sound on a surface area perpendicular to the direction of the sound.

The Sound Pressure

The Sound Pressure is the force (N) of sound on a surface area (m²) perpendicular to the direction of the sound. The SI-units for the Sound Pressure are N/m² or Pa.

Sound is usually measured with microphones responding proportionally to the sound pressure - p. The power in a sound wave goes as the square of the pressure.

(Similarly, electrical power goes as the square of the voltage.) The log of the square of x is just 2 log x, so this introduces a factor of 2 when we convert to decibels for pressures. The difference in sound pressure level between two sounds with p1 and p2 is therefore:

The Sound Pressure Level

The lowest sound pressure possible to hear is approximately 2 10^-5 Pa (20 micro Pascal, 0.02 mPa), 2 ten billionths of a an atmosphere.

It therefore convenient to express the sound pressure as a logarithmic decibel scale related to this lowest human hearable sound - 2 10^-5 Pa, 0 dB.

The Sound Pressure Level:

L_p = 10 log( p² / p_ref² ) = 10 log( p / p_ref )² = 20 log ( p / p_ref ) (1)

where

L_p = sound pressure level (dB)

p = sound pressure (Pa)

p_ref = 2 10^-5 - reference sound pressure (Pa)

If the pressure is doubled, the sound pressure level is increased with 6 dB ( 20 log (2) ).

Recommended maximum sound pressure level in rooms with different activities.

The table below indicates the sound pressure level in decibel caused by some common sources.

Source	Sound Pressure Level (dB)
Threshold of Hearing
Quietest audible sound for persons with excellent hearing under laboratory conditions²⁾	0
Quietest audible sound for persons under normal conditions
	10
Rustling leaves	20
Noticeably Quit - Voice, soft whisper
Quiet whisper (1 m)	30
Home	40
Moderate
Quiet street	50
Loud - Unusual Background, Voice conversation 1 m
Conversation	60
Loud - Voice conversation 0.3 m
Inside a car Car (15 m) Vacuum cleaner (3 m) Freight Train (30 m)	70
Loud singing	75
Loud - Intolerable for Phone Use
Automobile (10 m) Maximum sound up to 8 hour (OSHA criteria - hearing conservation program) Pneumatic tools (15 m) Buses, trucks, motorcycles (15 m)	80
Motorcycle (10 m)	88
Food blender (1 m) Maximum sound up to 8 hour (OSHA¹⁾ criteria - engineering or administrative noise controls) Jackhammer (15 m) Bulldozer (15 m)	90
Subway (inside)	94
Very Loud
Diesel truck (10 m)	100
Lawn mower (1 m)	107
Pneumatic riveter (1 m)	115
Threshold of Discomfort
Large aircraft (150 m over head)	110
Chainsaw (1 m)	117
Deafening, Human pain limit
Amplified Hard Rock (2 m) Siren (30 m)	120
Jet plane (30 m) Artillery Fire (3 m)	130
Short exposure can cause hearing loss
Military Jet Take-off (30 meter)	150

¹⁾ OSHA - Occupational Safety and Health Act - The OSHA criteria document reevaluates and reaffirms the Recommended Exposure Limit (REL) for occupational noise exposure established by the National Institute for Occupational Safety and Health (NIOSH) in 1972.

The REL is 85 decibels, A-weighted, as an 8-hr time-weighted average (85 dBA as an 8-hr TWA). Exposures at or above this level are hazardous.

²⁾ The reference level - 10^-12 - for the decibel scale.