Please wait for the animation to completely load.

This applet calculates seven frames and then runs continuously. For a large number of sources, or for very small wavelengths, this calculation can take some time, so let the applet finish calculating all seven frames.

The animation depicts a ripple tank in which you can see interference effects with two or more sources. When two or more waves encounter each other, they interfere. Waves can interfere constructively, resulting in a larger amplitude at a particular point, or they can interfere destructively, resulting in a smaller amplitude.

Sources of waves are shown by red dots. The waves are represented in black and white. The location of the sources can be changed by click-dragging on the source in the animation. New sources can be added using the text boxes and the "add source" button, and the wavelength of the sources can be changed by using the wavelength text box and the "set wavelength and play" button.

In the amplitude view (select the "show amplitude view" button) the greatest amplitude is represented by white, negative amplitudes are represented by black, and areas with zero amplitude are represented by gray. Note that in a real ripple tank, this is the view you would see.

In the intensity view, where the intensity is proportional to the square of the amplitude, the greatest magnitude of the amplitude (positive or negative) is represented by white, while black shows regions of zero amplitude. This is precisely because the intensity is related to the square of the amplitude. Note that when we are looking at light waves on a screen, this is the view that you would see. Since the energy of the wave is proportional to the square of its amplitude, we could also interpret the intensity mode as the energy mode.

There are several important features we need to understand about this animation and the two representations. First let's consider one source. Clear sources and add a source at the origin with an amplitude of 1 and 0 phase. Also set the wavelength to 1. Look at the amplitude view by clicking the button and waiting for all seven frames to load. Measure the wavelength.  Obviously you should get 1. This is the distance between adjacent white or black regions. Now change the view to the intensity view and again wait for all seven frames to load. Again measure the wavelength. Again you should get 1. Did you?   You may not have. In the intensity view the wavelength is not the distance between adjacent white or black regions. You need to include one more white region or black region to get the wavelength. This is because, in the amplitude mode, the series of white and black regions represent amplitudes of +  -  +   -  +   -  +  -, etc. However, in the intensity mode, the series of white and black regions represent intensities of  +  0  +  0  +  0  +  0, etc. but correspond to amplitudes of  +  0  - 0  +  0  -  0, etc., since the intensity is related to the square of the amplitude. If this is confusing (or even if it is not), consider the pictures below and notice that they give the same wavelength as long as you realize the difference in interpretation.

amplitude mode:
+ represents an amplitude of +1

intensity mode:
+ represents an amplitude of +1

Now clear your source and add two sources with the same phase and amplitude 1 position unit apart at y = 0 (x = -0.5 and x = 0.5). Set the wavelength to 2 position units and play the animation. Notice how you get dead spots due to interference to the right and the left of the sources on the y axis. Why does this happen? Since the separation between the sources is one half of a wavelength for any position on the x axis, the two waves will always be 180° out of phase and destructively interfere. Also note that on the y axis the two waves are equidistant from any position on the y axis and, therefore, the two waves constructively interfere (the two waves are always in phase). Hence, when we have interference, we are seeing that path difference creates a phase difference between the two waves.

You can also use the animation to further explore the properties of waves.

• What happens if the distance between the sources is increased or decreased?
• What happens if the phase between the sources is changed?
• What happens if the wavelength of the emitted waves is increased or decreased?
• What happens if more sources are added?

Illustration authored by Mario Belloni and Melissa Dancy.