Re: Sound Cancellation

["Polvani, Donald G." <donald_g_polvani@MD.NORTHGRUM.COM>]

John Denker wrote:

> The way it really works is that if the waves interfere
> destructively at one place (leading to the law 1 and 1
> makes zero) they will interfere constructively at some
> other place (leading to the law 1 and 1 makes 4).  So
> if we average over all locations, we get the law that
> 1 and 1 makes 2 on the average.

Here is a conundrum which has bothered me since graduate school.  I have two
plane waves (EM or acoustic, or whatever).   They are ideal plane waves both
propagating to the right along the x axis at the same speed.  However, I
arrange their phases so that the are exactly 180 deg out of phase.  Since
they travel at the same speed, and are single frequency waves, they should
maintain their 180 deg phase difference at all points in space.  I see no
way that they will interfere destructively along some portion of the x axis
and constructively along some other portion.  Furthermore, this perfect
cancellation persists for all time.  Each plane wave carries average energy
(which I take here to be proportional to the square of its amplitude).
However, the sum of the two plane waves has zero amplitude at all points in
space and, therefore, zero average energy.

How do I get out of my conundrum?  Have I, by construction of two waves
perfectly out of phase everywhere, and at all times, just constructed an
unnecessarily complicated way of saying there were, effectively, NO waves
there in the first place (i.e. I've just said that 1 + (-1) =0)?  If not, I
can do my construction for all of the infinititely possible directions of
propagation, always using two perfectly out of phase plane waves, and
construct a space with an infinite average energy from one viewpoint and
zero average energy from the other.

Don Polvani
Anne Arundel Community College
Arnold, MD
(Who is too old to go back to school, but still has some things he would
like to learn)