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