Hi!
In my wave mechanics class, we derived that the time-average intensity of a sound wave, is given by
,
whereis the wave speed,
is the density,
is the displacement amplitude and
is the angular frequency.
The derivation seemed allright, but in the next sentence the lecturer stated the minimum audible intensity of sound is(a figure supported by other sources, and concluded from the above formula that
(with
,
, and
). This value equates to about a tenth of the radius of a hydrogen atom, so surely there must be some flaw to the argument. I and my fellow students supposed that the problem lies in the formula being derived from a macroscopic point of view, where the air is treated as a continuous medium, rather than a discrete medium consisting of molecules (which effect must certainly be present at displacement amplitudes corresponding to the low intensity of
.
Would anybody care to shed some light on this issue?
Thanks!