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# Sound Power

## Sound power from sources like fans, jet engines, cars, humans and more.

### Sound Power (W)

Sound power is the energy rate, or energy of sound per unit of time (J/s or W in SI-units) - emitted by a source.

When sound propagates through a medium acoustic sound power is transferred. The sound intensity is the sound power transmission through a surface (W/m2) - a vector quantity with direction through a surface. The sound power radiated from a source can therefore be calculated by integrating the acoustic intensity over a surrounding surface.

N = S  I·n dS                         (1)

where

N = acoustic power radiated from source (W)

I = sound intensity - sound power through surface (W/m2)

n = unit vector normal to surface area

S = surface area surrounding source (m2)

For a source propagating sound in all directions - through a virtual spherical surface - the acoustic power can be modified to

N = 4 π r2 I                         (1b)

where

r = radius in sphere  (m)

### Sound Power Level (dB)

It can be practical to express the sound power relative a reference power - 10-12 W - in a logarithmic "decibel" scale as

LN = 10 log10(N / Nref)

= 10 log10(N) + 120                          (2)

where

LN = sound power level (decibel , dB)

N = sound power (W)

Nref = 10-12 - reference sound power (W)

The human ear is able hear sound powers that spans from 10-12 W to 10 - 100 W, a range of 10/10-12 = 1013.

#### Example - Sound Power Level

The sound power from a from a tool is 0.0015 W. The sound power level can be calculated as

LN = 10 log10 ((0.0015 W) / (10-12 W))

= 91.8 dB

The sound power level from a machine is rated to 100 dB. The sound power can be calculated by rearranging (1) to

N = 10((LN - 120) / 10)

= 10(((100 dB) - 120) / 10)

= 0.01 W

### Sound Intensity Level (dB)

Sound intensity can also be expressed relative to a reference intensity - the threshold of hearing - 10-12 W/m2 - in a logarithmic "decibel" scale as

LI = 10 log10(I / Iref)

= 10 log10(I) + 120                          (3)

where

LI = sound intensity level (decibel , dB)

I = sound intensity (W/m2)

Iref = 10-12 - reference sound intensity (W/m2)

The value of sound intensity level and sound pressure level is almost the same

LI = Lp - 0.2            (4)

where

Lp = sound pressure level (dB)

#### Example - Sound Intensity and Pressure Level - Distance from Source

The sound intensity - sound power transfer per unit surrounding surface - in a distance 1 m from the 100 dB machine in the example above can be calculated by rearranging (1b) to

I =  N / (4 π r2)

= (0.01 W) / (4 π (1 m)2)

= 0.0008 W/m2

The sound intensity level can be calculated with (3) as

LI ≈ Lp 10 log10(0.0008 W/m2) + 120

= 89 dB

The sound intensity in distance 10 m

I =  N / (4 π r2)

= (0.01 W) / (4 π (10 m)2)

= 0.000008 W/m2

The sound intensity level can be calculated with (3) as

LI ≈ Lp10 log10(0.000008 W/m2) + 120

= 69 dB

### Typical Sound Power

Sound power in watts and sound power level in decibels from some common sources are indicated below:

SourceSound Power
- N -
(W)
Sound Power Level
- LN -
(dB)
(ref 10-12 W)
Saturn Rocket 100,000,000 200
Turbo Jet Plane Engine 100,000 170
10,000 160
Inside jet engine test cell
Jet Plane Take-off
1,000 150
Large centrifugal fan, 800.000 m3/h
Turbo Propeller Plane at take-off
100 140
Axial fan, 100.000 m3/h
Machine Gun
Large Pipe Organ
10 130
Large chipping hammer
Symphonic orchestra
Jet Plane from passenger ramp
Heavy Thunder
Sonic Boom
Small aircraft engine
Tractor 150 hp
1 120
Centrifugal fan, 25.000 m3/h
Accelerating Motorcycle
Heavy Metal, Hard Rock Band Music
Chain Saw
Wood Working Shop
Large air Compressor
Electric motor 100 hp/2600 rpm
0.1 110
Air chisel
Subway Steel Wheels
Magnetic drill press
High pressure gas leak
Banging of steel plate
Drive gear
Car at Highway Speed
Normal Fan
Vacuum Pump
Banging Steel Plate
Wood Planer
Air Compressor
Propeller Plane
Outboard motor
Loud street noise
Power Lawn Mover
Pneumatic drill
Helicopter
0.01 100
Cut-off saw
Hammer mill
Small air compressor
Grinder
Heavy diesel vehicle
Heavy city traffic
Lawn mover
Airplane Cabin at normal flight
Kitchen Blender
Spinning Machines
Subway train
Pneumatic Jackhammer
0.001 90
Alarm clock
Vacuum Cleaner
Dishwasher
0.0001 80
Toilet Flushing
Printing Press
Noisy Office
Inside Automobile
Clothes Dryer
0.00001 70
Large department store
Busy restaurant or canteen
Ventilation Fan
Noisy Home
Average Office
Hair Dryer
0.000001 60
Room with window air conditioner
Office Air Diffuser
Quiet Office
Average Home
Quit Street
0.0000001 50
Voice, low
Small Electric Clock
Private Office
Quiet Home
Refrigerator
Bird Singing
Ambient Wilderness
Agricultural Land
0.00000001 40
Room in a quiet dwelling at midnight
Quiet Conversation
0.000000001 30
Rustling leaves
Empty Auditorium
Whisper
Watch Ticking
Rural Ambient
0.0000000001 20
Human Breath 0.00000000001 10
0.000000000001 0

## 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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