Instructions - Superposition of Waves Calculator

Purpose:

The Superposition of Waves Calculators show the result of adding two or more waves of the form:

Some of the calculators allow for the visualization of time dependent waves of the form

Finally, the wave packet visualizaler allows for the calculation of the superposition of waves with a range of wave number, with amplitude for each wave number defined by an "envelope function" A(k), where the user has the choice of plotting

or

where

General Information:

1. For all calculators
   • Select the checkbox above a components options to add or remove components into the resultant wave
   • Use the sliderbars or enter into the text fields to change the amplitude, wave number, or phase of each component. If you use the text field, you must hit enter or tab after entering your value.
   • Press the "fit graph in box" button to auto scale the bounds of the graph box
   • Press the "set graph limits" button to set the maximum and minimum values of the y range in the graph box
2. For time dependent calculators
   • Enter the time you wish to see the wave evaluated at in the text area next to the "time" label. You may also use the slider bar provided.
   • If you use the "double arrow" buttons on the slider bar, you will animate the graph starting from the current time, moving towards the minimum or maximum time allowed by the slider bar.
3. For wave packet calculator
   • Enter in the envelope function as a function of "k". A typical function would be one that is large near some expected value of k, and drops off as k is larger or smaller than the expected value. For example, "exp(-(k-50)**2.0)" would be a Gaussian centered around k=50.
   • Enter in the range for the integration of k.
   • Enter in the number of points to be used in the integration.