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# 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 (m2) perpendicular to the direction of the sound.

• the SI-unit for sound pressure is Pa or N/m2

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:

Lp = 10 log (p2 / pref2)

= 10 log (p / pref)2

= 20 log (p / pref)                                      (1)

where

Lp = sound pressure level (dB)

p = sound pressure (Pa)

pref = 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.

Download and print 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

pe = pa / 21/2                                      (2)

where

pe = measured (effective) pressure  (Pa)

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

### Sound Pressure Levels

Sound pressure levels in decibels from some typical sources:

SourceSound 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
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 (OSHA1) 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

### 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:

La = 10 log (1/n (100.1 L1 + 100.1 L2 + ... + 100.1 Ln))

where

La = average sound pressure level (dB)

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

n = number of sources

## Related Topics

• Acoustics - Room acoustics and acoustic properties, decibel A, B and C, Noise Rating (NR) curves, sound transmission, sound pressure, sound intensity and sound attenuation.
• Noise and Attenuation - Noise is usually defined as unwanted sound - noise, noise generation, silencers and attenuation in HVAC systems.

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## Unit Converters

Temperature

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Length

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Area

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3 30

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