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Slide 48

Sound Level in Decibels

Sound Level in Decibels

The greater the intensity of a sound at a certain place, the louder it will sound. But doubling the intensity will not make it seem twice as loud. Experiments show that the intensity must increase by about a factor of 10 before the sound will seem twice as loud to us. A sound with a 100 times greater intensity will sound about 4 times louder. Therefore, we measure sound level (loudness) based on a logarithic scale. The sound level in decibels (dB) is given by:

Ex: At a certain distance from a siren, the intensity of the sound waves might be 10 5 W / m 2 . The sound level at this location would be:

Note: According to this definition, a sound at the intensity level registers zero decibels:

(in decibels)

10 log (10 5 / 10 12) = 10 log (10 7 ) = 70 dB

10 log (10 12 / 10 12) = 10 log (1 ) = 0 dB

Slide 49

The Decibel Scale

The Decibel Scale

Pain

Damage

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Constant exposure leads to permanent hearing loss.

The chart below lists the approximate sound levels of various sounds. The loudness of a given sound depends, of course, on the power of the source of the sound as well as the distance from the source. Note: Listening to loud music will gradually damage your hearing!

Slide 50

Intensity & Sound Level

Intensity & Sound Level

Every time the intensity of a sound is increased by a factor of 10, the sound level goes up by 10 dB (and the sound seems to us to be about twice as loud). Lets compare a 90 dB shout to a 30 dB whisper. The shout is 60 dB louder, which means its intensity is 10 to the 6th power (a million) times greater. Proof:

60 = 1 - 2 = 10 log (I 1 / I 0 ) - 10 log(I 2 / I 0 ) = 10 log

60 = 10 log (I 1 / I 2 )

6 = log (I 1 / I 2 )

10 6 = I 1 / I 2

Compare intensities: 80 dB vs. 60 dB

Compare intensities: 100 dB vs. 75 dB

Compare sound levels: 4.2 10 4 W / m 2 vs. 4.2 10 7 W / m 2

answers:

factor of 100

factor of 316 (10 2.5 = 316)

differ by 30 dB ( Is differ by 3 powers of 10 )

Slide 51

Decibel Example

Decibel Example

Suppose a 75 g egg is dropped from 50 m up onto the sidewalk. The splat takes 0.05 s. Nearly all of the gravitational potential energy the egg had originally is converted into thermal energy, but a very small fraction goes into sound energy. Lets say this fraction is only 6.7582 10 11. How loud is the splat heard from the point at which the egg was dropped? Hints: Answers:

How much energy does the egg originally have?

How much of that energy goes into sound?

Calculate sound power output of the egg.

Figure intensity at 50 m up. (Assume the hemispherical wavefronts.)

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