An applet to explore standing waves.
Let us consider the following waves
y1 = a cos (wt  bz) and y2 = a cos (wt  bz)
These two waves travel in the same direction. If you add these two waves, you obtain another travelling wave of the form y = 2 a cos (wt bz).
Let us now consider the following waves
y1 = a cos (wt  bz) and y2 = a cos (wt + bz)
Note that because of the terms wt  bz and wt + bz, the two waves travel in opposite directions.
If we now add the two waves
y = a cos (wt  bz) + a cos (wt + bz)
= 2a cos (wt) cos (bz)
The terms containing the time and distance cos wt and cos bz are separated and therefore the wave obtained is not a travelling one. The applet below helps you gain a deeper understanding of standing waves.
TUTORIAL
1  click on the button above "click here to start" and MAXIMIZE the window obtained.
2  Click on the button "reset time".
3  Click on the button "increment time by steps" slowly and continuously in order to understand that the two waves (one in blue and the second magenta) are travelling in opposite direction. Also observe that the sum of the two waves (in black) does not travel: the maximums and minimums do not change position.
4  Click now on the button "START/STOP animation" to clearly see the two waves moving in opposite direction and the standing wave.

