# Constructive and destructive interference

#### Cypher04

To start with, this is not part of any homework assignment, and I am not looking for any numerical answer. Also, understand that I am a geology major, I have rocks for brains.
I have been looking at interference when waves interact. I found a basic simulator here: https://phet.colorado.edu/en/simulation/wave-interference, and I have been wondering about the math behind it. I have gathered that frequency, amplitude and the distance between the point source are all taken into account at least on the 2D level, but I do not understand how. I am also wondering about what the effect of a time separation between the activation of the sources would be and how I would calculate that. I would appreciate just a quick rundown of the equation for this. I will also be looking at this with more than 2 sources and I would like to look at it in 3d with 5 or more scores.

I think that the topic that suits your question best is Acoustic wave equation, you can even look for it in wikipedia where it have also 3d treatment.
The effect of time separation between sources will cause different phase between the sources which will change the interference pattern (in case of single frequency) such that the minimum and maximum points will be shifted.
If you just have sources without diffractions it should be simple to calculate as at each point you just sum the exponents of the sources where the amplitude depends on the one over distant squared and the phase depends on the propagation time.

#### Woody

I usually find Wikipeda a good source of reasonably pitched information for these sort of queries.
Try <Wkipedia : Wave Interference>

There is all sorts of detail to consider, (phase amplitude wavelength)
but the fundamental issue is just the summation of 2 (or more) sinusoidal functions.

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