Path Different Between Two Waves

[Bashyboy]

Hello,

I am having a little difficulty articulating my question, so please bear with me. I understand that when waves occupy the same space at the same time, they interfere. What I am having difficulty visualizing is when two different waves travel different paths and intersect at some point; in particular, when they reflect of surfaces at certain angles, etc. To give some context, I am reading about compton scattering and x-rays at the moment, and they are assert if the difference in path lengths of two lights of the same frequency are some integer multiple of their wavelength, then if they intersect at some point in time in space, they will interfere constructively.

If anyone knows of a simple way of explaining this, and perhaps has some visual aid that I could not find on the internet, I would be very grateful

 

[Simon Bridge]

What I am having difficulty visualizing is when two different waves travel different paths and intersect at some point;

Sounds like you need to play with small ripples in the bathtub sometime.
It is simple enough to make small waves that travel in different directions - because they overlap at an angle, the constructive and destructive interference pattern can get quite complicated.

If the path-difference from the sources to where you are looking is zero - can you see that you get maximum amplitude there? (The wave still bobs up and down.)

If you think of the wave as a series of pulses, and I send out pulse1 then pulse2 then pulse3 etc ... then the wavelength is the distance between peaks.
I have two sources, A and B, and I'll label the pulses from source A as A1, A2 etc and the pulses from source B are B1, B2 etc.

I also have a detector D which I can move around, it just tells me the amplitude of the pulses it sees.
The path length from A to D is |AD|, and from B to D is |BD|I start the sources at the same time so A1 and B1 leave at t=0, and they both travel at the same speed ... followed by A2 and B2 etc.

If D is situated exactly the same distance from A and B, (the path difference |BD|-|AD|=0) the A1 and B1 will arrive at the same time, so will A2 and B2 etc. You can see this will give constructive interference and maximum overall amplitude?

If I move D around, though, the pulses do not generally arrive at the same time.

If I move D just a bit so the distance to B is a bit more than the distance to A, then B1 arrives a bit later than A1. This is still constructive interference, but it is not maximum.

Keep making the distance to B a bit longer while keeping the distance to A the same and at some point B1 will arrive exactly half-way between A1 and A2... this is the minimum amplitude. A wave would have a trough there for destructive interference.

Keep making the distance to B a bit longer while keeping the distance to A the same and at some point B1 will arrive exactly when A2 does, and B2 will arrive when A3 does and so on - for constructive interference.
The path difference |BD|-|BA|= one wavelength.