Wave Interference Part 2- 2-dimensional Wave interference and PLD

Hey Everyone!

Now that we've talked about one-dimensional wave interference (standing waves) we can talk about something a little more complex: 2-dimensional wave interference.

In most situations, waves aren't interacting on a string, right? They tend to work across the surface of a two-dimensional space (think water waves). The two sources produce pulses at the same time, and for our purposes, with the same frequency and wavelength.

Remember how standing waves have nodes and antinodes? Well, this is true with 2D wave interference as well. The really cool thing about nodes or antinodes in two dimensions is that they line up! This forms a nodal line (or an antinodal one)! (see diagram below) Those weird grayish line on the diagram are nodal lines- they NEVER move!

A critical term to know when talking about 2D wave interference is path length difference. Essentially, the two waves produced by the two sources have to travel a certain distance to reach a given point. The absolute value of the difference between the distances traveled by both waves from the center to that point is the path length difference.

The highest possible value for the path difference is equal to the distance between the two sources (the source separation).  The lowest possible value is at any point that is equidistant from both sources (and is therefore equal to 0 wavelengths)

The formulas for Path length difference are:

Path length difference = |pathlength1 - pathlength2|

Path length = n * wavelength

Whoa, hold it. What the heck is n? Where did THAT random variable come from? Essentially, n is the path length difference in terms of wavelength.

When n is a whole number, an antinodal line exists. When n ends in ____.5, a nodal line passes through that point.

See diagram or "di a" ... never mind. You see what I did there? Red lines are antinodal, blue are nodal, and green (should be red) is the line of source separation.

The last thing I'm going to talk about before I let you amazingly patient people go to bed are the EQUATIONS we can use.

path length difference = n* wavelength


v = f * wavelength

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