# Sound Pressure

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

### Sound Pressure *(Pa)*

The Sound Pressure is the force (*N*) of sound on a surface area (*m ^{2}*) perpendicular to the direction of the sound.

The SI-units for the sound pressure are *N/m ^{2}* or

*Pa*.

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.

### The 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. The minimum audible level occurs between

*3000 and 4000 Hz*. For a normal human ear pain is experienced at sound pressures of order

*60 Pa or 6 10*.

^{-4}atmospheresIt is convenient to express sound pressure with the logarithmic decibel scale related to the lowest human hearable sound - *2 10 ^{-5} Pa *or

*0 dB*.

Sound Pressure Level 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)

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

### Measuring Sound Pressure

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

*p _{e} = p_{a} / 2^{1/2} (2)*

*where *

*p _{e} = measured (effective) pressure (Pa)*

*p _{a} = maximum pressure amplitude in the sound wave (Pa)*

### Sound Pressure Levels

Sound pressure levels in decibels caused by some common 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 Audio-metric test room | 10 |

Rustling leaves | 20 |

Noticeably Quit - Voice, soft whisper | |

Quiet whisper (1 m) | 30 |

Home Quiet room | 40 |

Moderate | |

Quiet street | 50 |

Loud - Unusual Background, Voice conversation 1 m | |

Conversation at 1 m | 60 |

Loud - Voice conversation 0.3 m | |

Inside a car Passenger Car 80 km/h (15 m) Vacuum cleaner (3 m) Freight Train (30 m) | 70 |

Loud singing | 75 |

Loud - Intolerable for Phone Use | |

Automobile (10 m) | 80 |

Motorcycle (10 m) | 88 |

Food blender (1 m) Maximum sound up to 8 hour (OSHA ^{1)} criteria - engineering or administrative noise controls)Jackhammer (15 m) Bulldozer (15 m) Noisy factory Newspaper press | 90 |

Subway (inside) | 94 |

Very Loud | |

Diesel truck (10 m) Motor horns at distance of 7 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) | 120 |

Jet plane (30 m) Artillery Fire (3 m) | 130 |

Upper limit for unprotected ear for impulses | 140 |

Short exposure can cause hearing loss | |

Military Jet Take-off (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

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