The waves described by the functions


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


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