Consider two waves with equal frequency and amplitude, and .

The difference between these two waves can be computed as follows:

Now

so we may write:

where we have calculated a new angle using

These equations are consistent as a consequence of the division by .

Hence the maximum value of the difference is , which is achieved at

Thus given the maximum distance apart of two out-of-phase but otherwise identical oscillators, we simply say:

Finally, in the case of the maximum being half the amplitude,