Bonus for those who want to play with Helmholtz's equation; an "eliptic" ordinary differential equation.
HelmholtzPlay is a visualization of a standing wave between the ground and the Ionosphere.
One can decide where the real value derivative of the standing wave equals zero and one can select
the strength and sign of the energyflow.
The yellow button points out the place and the little horizontal line below it indicates the size and direction of the flow.
The point can be moved by clicking on "place++" or "place--".
The change of the direction and its size can be made by clicking on "flowDirection++" and "flowDirection--".
The amount of changing when stepping can be altered by changing the value for the logDiff button.
One or two "zeropoints" for the "Wave index" can be used. When two points are used the difference between them
can be altered.
The physics behind is a generation of a wave generated upwards at the ground and
later reflected up in the ionosphere.
Above the reflection point there should be an evanecent wave "damped" when going upwards (to the right).
If the mathematics has not the correct balance a very large amplidue wave is comming from the outer space and
pass the ionosphere as an evanecent wave and below the reflectionpoint there will be
an ordinary travelingwave contributing to the standing one.
Do have a nice bonus time!
Ready made experiment
It is about a wave coming from the left. It is reflected and also damped by collisions.
The growing wave to the right is an artifact due to the almost impropely post problem;
an initialvalue problem from the left with exponential characteristics to the right!
The nearly infinitesimal missmatch demands an evanecent wave system from the right!
There is a aproximate standing wave just to left of the reflexion point.
End of April 2001
christer juren