Core Unit II: Wave Motion
B. Wave Phenomena

1. Transmission, Reflection, and Refraction

Key Concepts

Waves travel at a constant speed in a uniform medium. A change in medium, or a change in the condition of a medium, will usually result in a change in the speed of the wave.

A change in the speed of a wave results in a corresponding change in wavelength. The frequency of the wave remains constant once the wave has been generated.

The wavelength of a wave varies directly with the speed for any given frequency in the same medium.

In a fixed medium, where the speed of a wave remains constant, the wavelength varies inversely with the frequency. A change in frequency will result in a corresponding change in wavelength.

The amplitude of a wave depends on the amount of energy being transmitted. A decrease in the amplitude of a wave (as in a pulse travelling along a spring) indicates that energy is being dissipated, primarily due to frictional forces.

Fixed-end reflection results in an inverted pulse.

A decrease in the amplitude of a reflected pulse could indicate that energy has been transferred to the barrier (i.e. damping has occurred).

There is no inversion of a pulse in free-end reflection .

If a wave travels from one medium to another, it will experience partial reflection (and refraction) at the boundary between the two media.

Straight waves in a ripple tank striking a straight barrier observe the laws of reflection.

The angle of incidence is equal to the angle of reflection . The incident direction of propagation, the normal, and the reflected direction of propagation are coplanar.

When circular water waves strike a straight or curved barrier, the laws of reflection still apply, but the pattern becomes more difficult to analyze.

Waves reflecting from a parabolic reflector pass through the principal focus. This concentrates the wave energy. Many important applications make use of this phenomenon.

The behaviour of straight and circular water waves can be observed advantageously with a stroboscope.

When a wave enters a medium in which it moves more slowly, its wavelength decreases. The relationship between speed and wavelength is given by:

because and f remains constant.

For a specific change in medium, the ratio has a constant value.

(Further development of Snell's Law and the concept of the index of refraction could be covered here or in Core Unit III, Section C dealing with refraction.)

Learning Outcomes

Students will increase their abilities to:

1. Define the following terms: medium, amplitude, fixed-end reflection, free-end reflection, partial reflection, boundary, angle of incidence, angle of reflection, normal, barrier, parabolic reflector, stroboscope, refraction.

2. Explain that waves travel at a constant speed in a uniform medium.

3. Explain that a change in medium or a change in the condition of a medium will usually result in a change in the speed of a wave passing through that medium.

4. Suggest how the condition of a particular medium could be changed.

5. Explain that the frequency of a wave depends on the source which produced it.

6. Describe the changes in wavelength and speed that occur when waves travel from one medium to another.

7. Explain the relationship between speed and wavelength for periodic waves experiencing refraction.

8. Explain the relationship between frequency and wavelength for waves in a fixed medium undergoing a change in frequency.

9. State the laws of reflection.

10. Explain how the laws of reflection apply to straight water waves reflecting from a straight barrier.

11. Demonstrate an understanding of wave transmission, reflection, and refraction by relating these phenomena to practical and common experiences.

12. Interpret the relationship between speed and wavelength for waves undergoing refraction.

13. Apply problem solving techniques to the relationship between speed and wavelength for waves undergoing refraction.

Teaching Suggestions, Activities and Demonstrations

1. The usual ripple tank experiments described in most physics textbooks are ideal in this section. They provide concrete examples of wave behaviour.
   • Observe and describe the transmission, reflection, and refraction of water waves under a variety of different conditions.
   • Observe and describe the reflection of straight and circular water waves from straight and curved barriers.
   • Examine what happens when waves are reflected from a parabolic reflector.
   • Demonstrate, or have students investigate, partial reflection and refraction of a wave at a boundary.

2. Observe and describe reflection occurring in a one dimensional medium from fixed and free ends.

3. Suggest a plausible explanation for the decrease in amplitude experienced by a pulse travelling along a spring or some other one dimensional medium.

4. Collision ball apparatus are useful for investigating longitudinal energy transfer. They show a wave being propagated through a medium without transferring the medium.

5. Suspend a slinky from the ceiling. Send transverse and longitudinal pulses on the spring. Compare this to what happens when the pulses are sent along the spring when it is placed in a horizontal position along the floor. (The horizontal transverse wave pulses make a good analogy for polarization.)

6. Generate a standing wave pattern in a cup of water (or on some other object) placed on a vibrating surface.

7. Observe and describe periodic wave motion using a stroboscope.

8. Have students attempt to explain that the ratio remains constant for a specific change in medium.

9. To illustrate torsional wave motion, take a long string, about four metres in length, and tie ribbons to it at half metre intervals. Secure one end of the string. Give the other end a quick twist. The motion along the string can be observed by watching the ribbons move.