Re: [Phys-l] waves on a string

[John Denker <jsd@av8n.com>]

On 12/12/2010 06:41 PM, Al Bachman wrote:

>  "why does the energy at
> each point have to be constant ?" 

That depends on what "it" is.  In the Burko paper, the standing
wave had a constant energy at each point because it was, by
hypothesis, a standing wave.

For non-standing waves, which is most of the waves in the world,
the energy changes like crazy.

>  There ought to be a longitudinal standing density
> wave as well as the transverse wave. 

When considering transverse waves on a string, it is usual
to make the small-amplitude approximation, or more specifically
dy/dx << 1.  Then the coupling to the longitudinal modes is
small squared.

If you are sufficiently motivated, you can model the coupling
using perturbation theory.