# Two point sources produce waves of the same wavelength and are completely out of phase (that is...

## Question:

Two point sources produce waves of the same wavelength and are completely out of phase (that is produces a crest at the same time as the other produces a trough). At a point midway between the sources, would you expect to find a node or an antinode? Why?

## Constructive and Destructive Interference:

When two waves interact in such a way that the crests and troughs of the waves line up with one another (or are in phase) in the same pattern, the resulting interference pattern is known as constructive interference. Constructive interference will result points of maximum positive or negative displacement, known as antinodes. Conversely, when waves interact with one another such that they have opposite patterns (or are out of phase), the resulting pattern is known as destructive interference. Destructive interference will result in points of minimum displacement, known as nodes.

If two point sources produce waves of the same wavelength and are completely out of phase, at the midway point between the sources you would expect to find a node. The two waves are {eq}180^o {/eq} out of phase; therefore, at the midpoint one wave will be at a crest and the other at a trough. This pattern of interference is destructive interference, and as such, we would expect to find a node. 