Workout: Two-slit interference


Huygens' principle -- the math and Two-slit interference


the PhET simulation, Wave Interference

Set up

Select the "Waves" option from the entry screen.

When the sim comes up, it is set on the tab "Water" and is showing a faucet dripping into a tank of water. It's set dripping too slowly to make real sense of what's going on. Slide the "frequency" tab under the faucet about halfway to the maximum. Turn the faucet on by pressing the green button on the faucet. Let it run until the widow is filled with circles. Your screen should look like the figure below. 

Answer these questions

To get a better sense of what the dark and light bands mean, go to the right of the screen and slide the "Rotate view" slider bar all the way to the right. You should see light and dark bands in circles moving outward across the screen.

1. Pause the simulation. Then graph the water level monitor from the upper right corner of the control panel. It looks like the figure at the right. Each of the little rings measures the height of the water. The little graph at the right is a chart recorder. As time runs it records a graph of the height of the water at the position of the detector as a function of time. Place one of the rings of the detector in the center of a light ring and the other in the center of a dark ring. What can you conclude about the light and dark colors mean?

Let the simulation run. Describe what the graphs look like and what the difference in the two graphs are.

2. Pause the simulation. Remove the height detectors from the simulation pane and click on the "Graph" box. What is this graph showing? Explain why you think so.

Now let the simulation run. Describe what is happening on the graph and what it is representing.

3. Now go to the black tab bar on the bottom of the screen and select "Interference". You should now have two faucets. Pause the simulation, then turn on both faucets and start the sim. (It has to be done in this order so both faucets are releasing drips at the same time.)

Pause the sim and turn on the "Graph" box. Describe what you see. Let the sim run. How does the graph look the same or different from what you saw in part 2? 

4. Uncheck the "Graph" box. Increase the frequency to maximum and run the sim for a while. Pause the sim. Then move the height detector so that one of the detector is along the right of the box right in the center vertically and the other is along the right of the box along one of the "rays" that seem to go out from the center. Your screen should look like the figure on the right.

Let the sim run. Describe what the two height graphs look like. What's similar or different between them? Why are they like this?

5. Remove one of the detectors from the sim area and, while the sim is running, slowly slide the other detector from the top of the right wall of the sim area to the bottom. How many places along that wall are there where there is a maximum amount of oscillation and how many places where there is almost no oscillation?

6. The separation of the faucets is set by default at 3 cm. Before you make any changes, make a prediction: if you change the separation to 1 cm or 5 cm, for which would there be more places along the right wall where there is almost no oscillation? Then do the experiment and describe what you see. Was your prediction correct?

Joe Redish 7/5/19



Article 731
Last Modified: July 10, 2019