Core Unit II: Wave Motion
B. Wave Phenomena

2. Diffraction and other Wave Phenomena

Key Concepts

In a dispersive medium, the speed of the waves depends on the frequency. Higher frequency waves are refracted in a slightly different direction than lower frequency waves.

Diffraction is the bending that occurs when a wave passes around the edge of an obstacle. (Slits are barriers having two edges.)

Waves having longer wavelengths are diffracted more than those with shorter wavelengths.

When waves pass through a slit, diffraction is maximized when the wavelength and the slit width are within the same order of magnitude.

An interference pattern of water waves produced by two point sources vibrating in phase produces a symmetrical pattern of nodal lines and areas of constructive interference.

The interference pattern changes with different phase delays for the two point sources.

The phase of two repetitive events of the same frequency is the fraction of a period that one event leads ahead of or lags behind the other.

By drawing a series of uniform concentric circles (or by developing a computer simulation) representing circular waves produced from two point sources, one can develop a model to help explain the interference pattern of circular water waves created in a ripple tank. Regions of constructive and destructive interference become apparent on the model.

In a one dimensional medium, by controlling the amplitude and wavelength of incident and reflected waves, a standing wave interference pattern can be produced.

If the waves are allowed to pass continuously through one another, a set of nodal points and antinodes (loops) are produced.

The nodes are regions of maximum destructive interference. They are separated from one another by a distance of one-half of the wavelength of the interfering waves.

Antinodes (or loops) are regions of maximum constructive interference. They are separated by

½

and are separated from nodes by

¼

For a standing wave pattern on a one dimensional medium, the fixed ends are nodal points.

The distance between nodes can be altered by changing the frequency of the vibrating source.

The following conditions are necessary for a standing wave pattern to exist:

• There must be two waves of the same frequency. One or both of them may be a reflected wave.

• There must be a whole number of half wavelengths in the entire pattern.

Waves exhibit other properties such as scattering and polarization. (These topics could be developed here or in the section dealing with light.)

An understanding of wave behaviour has been beneficial to humankind in a variety of societal, techno- logical, and environmental applications.

Learning Outcomes

Students will increase their abilities to:

1. Define the following terms: diffraction, phase, nodal lines (nodes), antinodes (loops), standing wave pattern, resonant frequency, dispersion, dispersive medium, phase delay.

2. Explain that the speed of waves depends on the frequency in a dispersive medium.

3. Describe the two conditions that would lead to a maximization of the degree of diffraction experienced by waves.

4. Explain that nodal points are located one-half of the wavelength of the interfering waves from one another.

5. Explain standing wave interference patterns by relating them to an understanding of constructive and destructive interference.

6. Explain that the fixed ends of a one dimensional standing wave pattern must always be nodal points.

7. Explain that only certain resonant frequencies will produce standing wave interference patterns.

8. Explain that waves exhibit other properties such as scattering and polarization.

Teaching Suggestions, Activities and Demonstrations

1. Observe and describe the change in the interference pattern that occurs when two point sources are vibrating with different phase delays.

2. Place single and double slit barriers in a ripple tank. For a single slit, investigate the conditions under which diffraction is most pronounced. For the double slit, illustrate the interference pattern produced with a line drawing. Some students may be interested in writing a computer simulation of a double slit interference pattern.

3. Observe reflections from water, glass, plant surfaces, or metal through a polarizer. Look at the sky through a polarizer. Find the position in the sky relative to the sun where the maximum degree of polarization occurs.

4. Rotate two polarizers, one in front of another. Observe what happens. Place cellophane or clear plastic objects between two polarizers. Illuminate from below on an overhead projector. This illustrates an important industrial method used to examine photoelastic stress.

5. Look at a L.C.D. through a polarizer. Some students may have previously experienced this by examining a broken calculator that has a liquid crystal display.

6. Certain types of crystals exhibit interesting patterns when viewed with plane-polarized light. Investigate this phenomenon further.

7. Investigate other applications of polarizing materials.

8. Compare the effects produced by plane-polarizers and circular polarizers.

9. Observe a standing wave interference pattern produced in a one dimensional medium such as a stretched rope. Change the standing wave pattern by altering the frequency of the vibrating source.

10. Construct a graphic model or a computer simulation which can be used to analyze the interference pattern produced by two point sources.

11. Perform an activity to observe and describe the interference pattern produced when two point sources are vibrating in phase.

12. Look through the "slits" of a feather at an artificial light source. A diffraction pattern should be noticeable. A white feather works well for this activity.

13. Observe and describe the effect that changing either the wavelength or the slit width have on a resulting diffraction pattern in a ripple tank or using some other apparatus.