Power, Intensity, and Decibels

Power

• 3.846×1026 Watts of light

Light bulb

• 5 Watts of light

A speaker

Intensity

• ie. Loudness and brightness

Intensity of a uniform spherical wave

Intensity Ratio

A

B

Intensity Ratio

iclicker time• A concert loudspeaker suspended high above the

ground emits 35w of sound power. A small microphone with a 1.0cm 2 area is 50 m from the speaker. – What is the sound intensity at the position of the

microphone?

a) 0.035 W/m2

b) 0.0011 W/m2

c) 0.056 W/m2

d) 0.0045 W/m2

Decibels• Sound Intensity Level

Decibels -The Basics

• β = (10dB)log10(I / Io) • For the calculations that we are dealing with,

Io = 1.0 x 10-12 W/m2

• This is also known as the threshold of hearing• The symbol β is the Greek letter beta,

computed as a base-10 logarithm rather than a natural logarithm

Decibels

• The decibel is named after the inventor of the telephone, Alexander Graham Bell

• Decibels are only a name to remind us that we are dealing with an intensity level rather than true intensity

• Sound intensity level is actually dimensionless because it’s formed from the ratio of two intensities

How to calculate Decibels

• At the threshold of hearing, I = Io, where the sound intensity level is:

• β = (10dB)log10(Io / Io) = 0 dB• dB is just a way to measure the sound level,

and is completely arbitrary; it is not in any way a unit

• 0 dB does not mean no sound is produced, but rather means that to most people no sound is heard

Decibels (cont.)

• Since dogs have more sensitive hearing than humans, a 0 dB sound is easily heard by them

• As we all know, sound at a very high level can cause pain and ear damage

• The sound intensity level at the threshold of pain is β = (10dB)log10(10 W/m2 ÷ 10-12 W/m2) = 130 dB

Decibels

• The sound intensity level increases by 10 dB each time the true intensity increases by a factor of 10

• Studies indicate that when the intensity is increased by a factor of 10, the sound is perceived to be “twice as loud”

• The loudness of a sound is doubled with each increase in 10 dB

How Loud Is Too Loud?

• Even though the threshold of pain is 130 dB, quieter sounds can also cause serious ear damage

• Regular exposure of more than 1 minute of 110 dB risks permanent hearing loss

• 100 dB – no more than 15 minutes of unprotected exposure is recommended

• Prolonged exposure to any sound above 85 dB can cause gradual hearing loss

Just so you know• Decibels• 150• 120• 110• 105• 100• 95• 90• 85• 60• 40• 30• 0

• Sound Source• Firecracker• Ambulance siren• Chain saw, rock concert• Ipod at max volume• Wood shop, snowmobile• Motorcycle• Power mower• Heavy city traffic• Normal conversation• Refrigerator humming • Whispered voice• Threshold of human hearing

For teh lulz

• http://www.youtube.com/watch?v=oNz4oEqSvmc

• http://www.youtube.com/watch?v=ML_ySRkvyGQ

• http://www.youtube.com/watch?v=K58OOfRrGjs

Sources

• Images– http://www.flickr.com/photos/quatrosinko/93971967

4/sizes/l/in/photostream/– http://en.wikipedia.org/wiki/File:The_Sun_by_the_At

mospheric_Imaging_Assembly_of_NASA%27s_Solar_Dynamics_Observatory_-_20100819.jpg

– http://en.wikipedia.org/wiki/File:Gluehlampe_01_KMJ.png

– http://en.wikipedia.org/wiki/File:Lautsprecher_4-wege_2.jpg

– http://en.wikipedia.org/wiki/File:Sphere_wireframe_10deg_6r.svg

• Sources– Pearson. Physics for scientists and Engineers. 2008.

Nov 2011.– http://www.nidcd.nih.gov/health/hearing/pages/ruler

.aspx