CONTENTS Graphs: sine, cosine and tangent OTHER MATERIAL 
Wave Addition, Multiplication We can combine two wave functions to create more complex waves. For instance, the graphic below illustrates the results of adding a highfrequency, lowamplitude wave with a lowfrequency, highamplitude wave:
As you'd expect, this results in a highfrequency oscillation riding on top of the lowfrequency movement. The expression behind this addition (the last two lines are included only to make the WriteOn effect draw the wave properly): frequency_one=10 ; The results of multiplying one wave by another are considerably different. For starters, the resulting amplitude can be much higher than the amplitude of either component, so you'll often want to multiply relatively lowamplitude waves. The graphic below illustratres the results of multiplying a highfrequency wave by a lowfrequency wave (the amplitudes are comparable): You can see that this results in pulses of highfrequency, highamplitude oscillations. The expression behind this graphic (the last two lines again are included only to make the WriteOn effect draw the correct image): frequency_one=15; Applied to the spring animation used earlier, this compound wave looks like:

Entire contents © 2001 JJ Gifford.