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Re: Speed of Waves



On Sun, 28 Jan 2001, David Abineri wrote:

We are discussing mechanical waves (sound) and some students feel
(understandably at first) that the harder (faster) one 'hits' air
molecules, the faster the disturbance will travel through the air. They
are thinking that the air molecules are particles that simply move
faster when hit harder thus making the disturbance move faster..

What metaphor and explanation might help them to see that the medium
dictates the velocity regardless of the 'hit'.

You might start by reminding them that *they* could *never* begin
to hit the molecules very "hard" (in the sense of "fast") since
the molecules are already moving at hundreds of miles per hour.
Just holding your hand out already provides a spectacular "hit"
that can't be much improved on.

But then what about a supersonic plane? In this case the "hits"
are indeed substantial but the molecules that are hit, immediately
(within fractions of a millimeter) run into *far more* molecules
that are still loafing along. The excess kinetic energy is
quickly spread out and the only thing that remains is a
substantial *density variation* that propagates--like density
variations of any magnitude in a gas that is dominated by a small
mean free path--at a speed that is essentially determined by how
fast the molecules themselves are moving.

John Mallinckrodt mailto:ajm@csupomona.edu
Cal Poly Pomona http://www.csupomona.edu/~ajm