### Intensity and the Decibel Scale

A doubling of the distance from a noise source will reduce the sound pressure level with 6 decibel. Oct 27, Dear P students -- We have not yet talked about sound power, but on the amount of sound energy produced and the distance between. Sound and distance drop fall off damping noise We get a sound level drop of 6 dB per doubling of distance. Sound power or .. Relationship of acoustic sizes.

The decrease in intensity with increasing distance is explained by the fact that the wave is spreading out over a circular 2 dimensions or spherical 3 dimensions surface and thus the energy of the sound wave is being distributed over a greater surface area.

The diagram at the right shows that the sound wave in a 2-dimensional medium is spreading out in space over a circular pattern. Since energy is conserved and the area through which this energy is transported is increasing, the intensity being a quantity that is measured on a per area basis must decrease.

The mathematical relationship between intensity and distance is sometimes referred to as an inverse square relationship. The intensity varies inversely with the square of the distance from the source. So if the distance from the source is doubled increased by a factor of 2then the intensity is quartered decreased by a factor of 4.

**Closer - A Short Animation About Long Distance Relationship**

Similarly, if the distance from the source is quadrupled, then the intensity is decreased by a factor of Applied to the diagram at the right, the intensity at point B is one-fourth the intensity as point A and the intensity at point C is one-sixteenth the intensity at point A. Since the intensity-distance relationship is an inverse relationship, an increase in one quantity corresponds to a decrease in the other quantity.

- Sound Power

And since the intensity-distance relationship is an inverse square relationship, whatever factor by which the distance is increased, the intensity is decreased by a factor equal to the square of the distance change factor.

The sample data in the table below illustrate the inverse square relationship between power and distance. Referring back to our earlier discussions, power is the time rate of change of energy and has units of Joules per second. We give a new name to this unit: The Watt is the unit of power.

### Sound Power and Intensity

We will introduce a logarithmic scale for sound power, just like we did for sound pressure, because our perception of sound loudness is logarithmic. The "units" of sound power level are in decibels. This is really a dimensionless quantity. We quote the sound power level in decibels to remind ourselves that its a logarithmic quantity with a specific reference power. Sound Intensity We haven't yet made contact with loudness.

To do so, we need a receiver of the sound energy produced from the source. Before we get there, we have to ask the question where does the sound power produced from the source go?

## Intensity and the Decibel Scale

The simple answer is, everywhere. Most sources of sound send sound waves out uniformly in all directions. What this means is that if we are a certain distance from a source of sound, say a jet taking off, we will hear the same loudness sound independent of where we listen: The loudness of the noise we hear depends only on how far we are from the source of sound. The geometrical shape that has all points equal distance away from a source is a sphere.

The loudness we hear depends on the ratio of the area of our sound collector to the total area of the sphere surrounding the sound source.

This motivates the introduction of another physical quantity associated with sound waves: The intensity of a sound wave depends on how far we are from a source. We now have something that relates to our perception of loudness. This means that we should introduce a logarithmic scale, once again.

Both sound pressure level and sound intensity level are purported to measure the same thing: