PhysicsLAB Resource Lesson
Sound Level Intensity

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The rate at which the wave energy from a sound source is transferred from one location to another is expressed in terms of its intensity. Mathematically, this relationship is written as

and is measured in watts/m2. Therefore, the intensities at two different locations from a sound source would be related according to this ratio
which simplifies to
Note, that this is an inverse square relationship. That is, if the distance to location, r2, is twice as far from the source as the distance to r1, then the intensity at r1 is 4 times greater than it is at r2.
Sound intensity is perceived by our ears as loudness, in the same fashion as a sound's frequency is perceived by our ears as its pitch. The threshold of human hearing has a value of 1 x 10-12 watts/m2 and is represented by Io. This means that in order for us to "hear" a sound, not only must it be within our range of hearing (20-20,000 hz) but it must also be of sufficient intensity.
The doubling of a sound's perceived loudness does not represent a doubling of the sound's intensity. To compare relative intensity levels, we use a logarithmic scale and reference the  threshold of sound as a standard for comparison. The equation used to calculate this relationship is
Some common sound levels in decibels (dB) are shown in the following table.
 1. Compare the intensity of the loudness of normal conversation to that of a soft whisper.

 2. What is the sound level in dB for a sound whose intensity is 5.0 x 10-6 watts/m2?

 3. What is the intensity of a sound which has a sound level of 35 dB?

 4. If the source of the sound in question #3 was 6 meters away from the listener, where should a second person stand with respect to the same sound source to hear at 60 dB?

Notice in the last example that you cannot compare decibels and distances; that is, saying that the sound intensity varies inversely as the square of distance from the sound source does NOT apply to decibel readings, it only applies to intensities measured in watt/m2.

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