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# Sound: Loudness and Intensity

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The intensity at a distance of 6.0 m from a source that is radiating equally in all directions is 6.0 Ãƒ- 10-10 W/m2. What is the intensity level in dB?

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Intensity:
Intensity of sound is the amount of energy incident per unit area per unit time normal to surface. The unit of intensity is W/m2.
From a point source the emitted energy will distributed uniformly in all direction and will fall uniformly on a spherical surface with source at center. If a point source emitting power P, then at a distance r from the source the intensity will be

Level of loudness:
Loudness of the sound is the effect of the sound on the ears of a person. The loudness of the sound heard by a person is varies with intensity of sound at that point but not uniformly. The loudness is proportional to logarithm of the intensity of sound.
There is a minimum intensity I0 of sound at a place to be heard by a person (varies person to person, for a normal person it is approximately 10-12 W/m2). The loudness of the sound of this minimum intensity is called Zero level of loudness.
The level of loudness L is thus given by the relation
[base is 10]
Thus for zero level of loudness we have

Subtracting above equation we get

Or
For the unit in bel the value of constant k is one and the equation becomes

The common unit of measure the level of loudness is one tenth of the unit bel called decibel dB and hence if the level of loudness is measured in dB above equation takes the form

P7. The intensity at a distance of 6.0 m from a source that is radiating equally in all directions is 6.0 Ã— 10-10 W/m2. What is the intensity level in dB? Please provide detailed explanation.
Solution:
The intensity of sound at the point is
I = 6.0*10-10 W/m2
And as we know the zero loudness level intensity is
I0 = 10-12 W/m2
Substituting the values in the equation above we get

Or
Or
Or
Or L = 27.8 dB

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