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)
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.
Measuring Sound Pressure
Most Sound Level Meters measures the effective sound pressure which can be expressed as
pe = pa / 21/2 (2)
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:
|Source||Sound Pressure Level|
|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
|Noticeably Quit - Voice, soft whisper|
|Quiet whisper (4 ft, 1 m)||30|
|Loud - Unusual Background, Voice conversation 4 ft, 1 m|
|Normal conversation at 4 ft, 1 m||60|
|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
Car driven at 105 km/h, 65 mph
|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
|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)
|Diesel truck (30 ft, 10 m)
Motor horns at distance of 7 m
|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)
|Chainsaw (4 ft, 1 m)
Very noisy work - boilermakers workshop, etc.
|Deafening, Human pain limit|
|Amplified Hard Rock (6 ft, 2 m)
Siren (100 ft, 30 m)
|Jet plane (90 ft, 30 m)
Artillery Fire (10 ft, 3 m)
|Upper limit for unprotected ear for impulses
Threshold of pain
|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 (10 L1/10 + 10 L2/10 + ... + 10 Ln/10))
La = average sound pressure level (dB)
L1 .. Ln = sound pressure level source 1 .. n (dB)
n = number of sources
Room acoustics and acoustic properties, decibel A, B and C, Noise Rating (NR) curves, sound transmission, sound pressure, sound intensity and sound attenuation.
Noise is usually defined as unwanted sound - noise, noise generation, silencers and attenuation in HVAC systems.
Logarithmic unit used to describe ratios of signal levels - like power or intensity - to a reference level.
Sound pressure filters that compensates for the hearing sensed by the human ear.
Physiological effects from low-frequency noise or vibrations.
The rules of logarithms - log10 and loge for numbers ranging 1 to 1000.
Maximum recommended sound pressure levels in rooms like kindergartens, auditoriums, libraries, cinemas and more.
An online Noise Rating (NR) calculator.
The Noise Rating (NR) Curve used to determine acceptable indoor environments for hearing preservation, speech communication and annoyance.
The phonetic alphabet used in international aircraft communications.
The transmission of outdoor sound through and around barriers - the Fresnel Number.
In a room the sound or noise will reach the receiver as direct and reverberant sound.
The logarithmic decibel scale is convenient when adding signal values like sound power, pressure and others from two or more sources.
Background noise frequencies that interferes with speech.
The attenuation in a room depends on the location of the sound source and the receiver - and the room constant.
An introduction to the nature of sound with frequencies, wave-lengths and octaves.
Shift in hearing threshold for men and women vs. age.
Room size, absorption characteristics - and attenuation in direct sound fields.
Introduction to decibel, sound power, intensity and pressure.
OSHA maximum A-weighted sound pressure levels allowed per day.
Doubling of the distance from a noise source reduces the sound pressure level with 6 decibel.
Satisfactory, difficult and impossible noise levels for telephone use in noisy areas.
Acoustic noise calculation procedure HVAC systems.