Definition of Intensity

The intensity (or energy flow) of a sound wave is the power (in energy/sec) transmitted through an area of 1m oriented perpendicular to (normal to) the propagation direction of the wave.[1 ]
Almost everyone knows that if they move away from a constant sound source, they perceive a decrease in loudness. Consider the following example:

Figure 2.1 Decrease in loudness over distance

Assume that a sound from a source propagates through 1m of air at 10m from the source. Looking at the diagram we can see that the power that is concentrated over 1m at 10m from the source, is spread over a larger area at the distance of 20m. The same amount of energy is spread over a larger area, so the intensity has decreased. Specifically, the area at 20m is 4m which is 4 times the area at 10m (1m), making the energy at 20m 1/4 the intensity that it was at 10m. That is:

where r is the distance from the source.

The sensation of loudness is determined by the intensity. The greater the intensity the greater is the perceived loudness. It is usual to symbolise intensity as I expressed in watt/m.

Human hearing falls roughly in the range 1 Watt/m (the loudest, called the Threshold of Feeling) to 10 Watt/m (the softest, called the Threshold of Hearing. 10 = 0.000000000001 . (12 decades.)

These two thresholds vary from individual to individual and depend on the particular frequency under consideration. The size of this range is tremendous ( a trillion values); The unit of watt/m produces very unwieldy numbers. For these reason and others, the units watt/m is impractical.

[1] The energy flow associated with a sound wave is the total mechanical energy (potential and kinetic energies associated with elastic oscillations of the medium) that is transferred during each second through a surface of unit area (1m) - expressed in Joule/m/sec or Watt/m. This is commonly called the intensity of the wave and is designated I.

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