The other variable characterizing the traveling wave is of course its
amplitude. As long as the medium remains linear the amplitude
can be what
ever you wish. The amount of energy propagated by the traveling
wave depends on its amplitude. The book discusses the energy
transport for waves on a taut string. For a sound wave the
amount of energy transported is measured in terms of
how much energy passes a unit area per time unit. This quantity
is called the intensity of the sound wave and by writing down the
kinetic energy associated with the displacement of the gas
it can be shown
that its value is
Here 
is the max deviation of pressure from the average.
The ear is sensitive to intensities from approximately 
W/m
to 1 W/m in the frequency range
50 Hz-10 kHz as detailed in the Figure 14.6 of the supplementary
literature (Cromer's book). Intensities higher than that cause permanent damage to the ear. It is interesting to note that
the pressure excursions are surprisingly small. We can calculate these from Eq. 41
which gives
Atmospheric pressure is 
N/m so the relative change in
pressure associated with a sound wave which our ears can handle
varies from 
to 
. Because our ears
handle such a wide range of intensities we use a logarithmic scale
to describe the intensity of sound. Namely rather than quoting
I directly in W/m we quote
is dimensionless but to indicate that we are using
it as a means of communicating the sound intensity we postfix
values for by dB short for deci-Bell. All this
is nothing more nor less than a definition which has gained
acceptance because it is handy. With it the sensitive range of the
ear goes from 0 dB to 120 dB.