## Interference

The waves described by the functions

and

can be added algebraically to produce the resultant wave

We can define new variablesandthrough the equations

we can write

The resultant wave above is a sinusoidal wave of the same frequency,with

and

For a standing waveandsince the reflected wave required for a standing wave to be formed undergoes a phase change ofon reflection.

which is not defined. Consideration of the sign of the numerator implies we may take