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/m^{2}. 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, r_{2}, is twice as far from the source as the distance to r_{1}, then the intensity at r_{1} is 4 times greater than it is at r_{2}.
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/m^{2} and is represented by I_{o}. 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. |