VIBRATING STRING
                                        
This slide show shows how two travelling waves generate a stationary wave.

A.   Travelling Wave
     This shows three waves simultaneously.  The top one travels to the left.
The bottom one travels to the right.  The middle one is the average of the top
and bottom, and is stationary.  In fact the top and bottom are the same
function, viz.

                               sin(x) + sin(2x),
                                        
each translated by an amount ã/6 per slide, while the domain is -4ã < x < 4ã.
The stationary wave is thus the function sin(x)cos(a) + sin(2x)cos(2a), where a
is a multiple of ã/6.

B.   Stationary Wave [0 : 2ã]
     This shows the stationary wave of (A) for 0 < x < 2ã.

C.   Stationary Wave [0 : ã]
     This shows the stationary wave of (A) for 0 < x < ã.

In each of these three cases you have the choice of stepping through a sequence
of slides one at a time, or having the computer do it continuously and
automatically (either slowly or quickly).  If you choose continuously, the
computer will do so until you press the END key.

When viewing the slides, the following keys are operational:

HOME      takes you to the first slide in the sequence you selected
END       takes you to the last slide in the sequence you selected
UP ARROW  takes you to the previous slide in the sequence you selected
F9        immediately quits the program

These keys do NOT operate like that while you are reading this document.

When you have finished reading this document, press Q to quit.