Particles and Waves

Interference as evidence of waves.

Is light a particle or a wave?

Particle collision

What happens when particles meet head on?

Choices...

  1. bouncing back away from each other.
  2. stopping dead in their tracks.
  3. moving through each other.

 

Wave pulses meeting

  1. bouncing back away from each other.
  2. stopping dead in their tracks.
  3. moving through each other.

Waves appear to move through each other

Wave addition - INTERFERENCE

It seems that two pulses can pass through each other. Where they meet, the resulting shape is like adding the height of one pulse plus the height of the other pulse, like this...

What will the height of the pulse be when these two pulses meet each other?

crossing

 

 



















Check out this simulation of what's supposed to happen:


Here's a very short movie of pulses on a slinky with two pulses on the same side of the slinky moving toward each other.

Sequential frames

Sequential frames from this movie show two pulses advancing towards each other, turning into a "higher" pulse where they meet, and then moving away from each other...


boat wakeAt each moment in time, a moving boat disturbs the water, sending a wave pulse out to the left, and another to the right. This is called the boat's wake.

If two boats go beside each other, what should be the height where the two wakes run into each other? Take a look: two-boat wake-surfing video. (FF to about halfway in to the video...)

Waves on the surface of water in 2-d

Dipping 2 fingers repeatedly into a tank of water yields this sort of pattern of interference.

Where two crests meet, the height of the wave should be twice as high as one. Where two troughs meet, twice as low.

Where a trough and crest meet, total cancellation.

In the accompanying diagram:

 

Interference patterns

We can pictorially calculate how this pattern should come out by marking up a diagram of the undisturbed waves from the two sources with
An observer standing at the right side of the pool would see large waves rolling in at points marked with an X, and no waves motion at points marked O.

Young's double-slit

Have the waves from just one source hit a screen with two openings in it. Each opening acts like a "source" in its own right. But now the two "sources" are always in synch with each other, and are guaranteed to have the same frequency (that of the original plane wave coming at the wall).

Lab preparation:

  1. Copy the IMPORT-able parameters below (highlight all the lines and "Copy" to the clipboard).
  2. Open up Paul Falstad's ripple tank simulator.
  3. Choose "Import/Export",
  4. In the window that opens up, Paste the parameters over top of the ones that are there, and click Import.
  5. You should see a plane wave advancing towards a rough "wall" with two openings in the wall. After the pattern has run for a while, note the spacing between the lines of destructive interference.
  6. Now, choose "Clear Walls". Set the Mouse option to "Edit Walls".
  7. Draw with your mouse a new wall that has two openings that are closer together than in the previous situation. Are the lines of destructive interference closer together or further apart than they were before?? Show your lab assistant your results...

There is a formula for the angular distance $\Delta \theta$ between destructive interference lines, (or between constructive interference lines, for that matter) in terms of the distance $d$ between the two slits (holes in the wall) which is:

$$\lambda=2d\sin\Delta\theta$$

The wavelength of the waves, $\lambda$ is a constant for what you've been looking at. Is this formula compatible with what you observed?

Initial parameters:

$ 0 189 10 2 true false 8 25 477 1
s 20 21
s 208 21
c 13833 0
w 16 0
l 29
w 61 0
l 111
w 13 0
c 15 0
w 20 0
l 10
c 59 0
l 1
w 30 0
l 62
w 5 0
l 10
w 7 0
c 43 0
l 2
w 4 0
l 5
c 139 0
w 14 0
c 5 0
w 6 0
l 4
c 152 0
w 48 0
c 37737 0

 

Image credits

Molly Ali, Siggimus, Patrick Moran,