# What is the resultant of two rectangular simple harmonic motions of the same frequency and...

## Question:

What is the resultant of two rectangular simple harmonic motions of the same frequency and unequal amplitude, but differing in phase by {eq}\frac{\pi}{2} {/eq}?

## Superposition:

Superposition is a means to combine two events into one resulting event. The most common use for this is with waves or waveforms. Any time you have superposition, you will have either constructive interference, where it grows larger, or you have destructive interference, where the wave shrinks in amplitude.

So what happens completely depends on the waves that you are given, however, the simple answer is that the waves undergo destructive interference. This will happen to some degree as you have two similar waves that are out of phase with one another. This will result in the two waves interfering with one another. In some cases, it will solely be destructive interference, but with long enough wavelengths you can have some areas of constructive interference. 