The equation involving such wave propagation is given by

The above equation has a solution of the form

where

Thus equation (5.37) satisfies wave eqn (5.36) can be verified by substitution.
corresponds to the wave traveling in the + x direction while corresponds to a wave traveling in the -x direction. The general solution of the wave eqn thus consists of two waves, one traveling away from the source and other traveling back towards the source. In the absence of any reflection, the second form of the eqn (5.37) is zero and the solution can be written as