Sound Pressure

Sound Pressure is the force of sound on a surface perpendicular to the propagation of sound.

Sound Pressure (Pa)

Sound Pressure is the sound force (N) acting on the surface area (m 2 ) perpendicular to the direction of the sound.

the SI-unit for sound pressure is Pa or N/m 2

Sound is usually measured with microphones responding proportionally to the sound pressure. 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.

Sound Pressure Level (decibels)

The lowest sound pressure possible to hear is approximately 2 10 -5 Pa (20 micro Pascal, 0.02 mPa) or 2 ten billionths of an atmosphere. This minimum audible level occurs normally between 3000 and 4000 Hz.

For a normal human ear pain is experienced at a sound pressure of order 60 Pa or 6 10 -4 atmospheres.

Due to this range it is convenient to express sound pressure with a logarithmic decibel scale related typically to the lowest human hearable sound - 2 10 -5 Pa or 0 dB.

Since the energy in the sound wave is proportional to the square of the pressure - the Sound Pressure Level in decibel can be expressed as:

L_p = 10 log (p 2 / p_ref 2 )

=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)

Doubling sound pressure (in Pa) - increases sound pressure level (in dB) with 6 dB(or 20 log (2)).

The chart below shows the sound pressure level decibel scale compared to the sound pressure Pascal scale.

Sound Pressure Level (dB) vs. Sound Pressure (Pa) Chart

Measuring Sound Pressure

Most Sound Level Meters measures the effective sound pressure which can be expressed as

p_e = measured (effective) pressure (Pa)

p_a = maximum pressure amplitude in the sound wave (Pa)

Sound Pressure Levels

Sound pressure levels in decibels from some typical sources:

Sound Pressure Levels typical Sources

Source	Sound Pressure Level (dB)
Threshold of Hearing
Quietest audible sound for persons with excellent hearing under laboratory conditions 2)	0
Quietest audible sound for persons under normal conditions
Virtual silence, Barely audible Audio-metric test room	10
Rustling leaves Mosquito	20
Noticeably Quit - Voice, soft whisper
Quiet whisper (4 ft, 1 m)	30
Home Quiet room Bird call	40
Moderate
Quiet street Quiet office Whispered speech	50
Loud - Unusual Background, Voice conversation 4 ft, 1 m
Normal conversation at 4 ft, 1 m	60
Laughter	65
Loud - Voice conversation 1 ft, 0.3 m
Inside a car Passenger car 80 km/h, 50 mph (50 ft, 15 m) Vacuum cleaner (10 ft, 3 m) Freight Train (100 ft, 30 m) Background conversation restaurant	70
Loud singing Car driven at 105 km/h, 65 mph Washing machine	75
Loud - Intolerable for Phone Use
Maximum sound up to 8 hour (OSHA criteria - hearing conservation program) Pneumatic tools (50 ft, 15 m) Buses, diesel trucks, motorcycles (50 ft, 15 m) Car wash (20 ft, 6 m) Road with busy traffic	80
Motorcycle (30 ft, 10 m)	88
Food blender (4 ft, 1 m) Maximum sound up to 8 hour (OSHA 1) criteria - engineering or administrative noise controls) Jackhammer (50 ft, 15 m) Bulldozer (50 ft, 15 m) Noisy factory Newspaper press	90
Subway (inside)	94
Very Loud
Diesel truck (30 ft, 10 m) Motor horns at distance of 7 m	100
Lawn mower (4 f t, 1 m)	107
Pneumatic riveter (4 ft, 1 m)	115
Threshold of Discomfort
Large aircraft (500 ft, 150 m over head) Power saw	110
Chainsaw (4 ft, 1 m) Very noisy work - boilermakers workshop, etc.	117
Deafening, Human pain limit
Amplified Hard Rock (6 ft, 2 m) Siren (100 ft, 30 m) Pneumatic chipper Drums	120
Jet plane (90 ft, 30 m) Artillery Fire (10 ft, 3 m)	130
Upper limit for unprotected ear for impulses Threshold of pain	140
Short exposure can cause hearing loss
Military Jet Take-off (100 ft, 30 meter)	150
Large military weapons	180

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 dB, A-weighted, as an 8-hr time-weighted average (85 dB(A) as an 8-hr TWA). Exposures at or above this level are hazardous.

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

Typical Subjective Description of Sound Pressure Level

0 - 40 dB : quiet to very quiet
60 - 80 dB : noisy
100 dB : very noisy
> 120 dB : intolerable

Sound power level common sources

Averaging Sound Pressure Level from a number of Sound Pressure Level Readings

The sound pressure level from a number of sound pressure level readings can be calculated as:

L_a = average sound pressure level (dB)

L₁ .. L_n = sound pressure level source 1 .. n (dB)

n = number of sources