PhysicsQuest

WAVE BEHAVIOR
INTRODUCTION

By the end of these activities you should have:

1. An understanding of the behavior of a pulse at the end of a medium, including free-end and fixed-end reflection and the transmission of a pulse from one medium to another medium with a different density.

2. An understanding of interference as a behavior which occurs as two waves interfere while moving through the same medium; an ability to distinguish between constructive and destructive interference; an ability to use the principle of superposition in order to determine the resultant shape and size of a wave pattern produced by two interfering waves.

3. An understanding of how a standing wave is formed from two individual interfering waves; an ability to diagram standing wave patterns of a tube with both ends closed; an ability to identify the nodes and antinodes in a standing wave pattern and to relate the length of the tube to the wavelength of the wave for any given harmonic.

4. An understanding of how a standing wave is formed from two individual interfering waves; an ability to diagram standing wave patterns of a half-closed tube; an ability to identify the nodes and antinodes in a standing wave pattern  and to relate the length of the tube to the wavelength of the wave for any given harmonic.
TASK

By visiting the links provided you will be able to answer the questions.
The PhysicsQuest is divided into three activities as follows:

I. BOUNDARY BEHAVIOR
Case 1. Fixed-End Reflection
Case 2. Free-End Reflection
Case 3. Thinner-to-Thicker
Case 4. Thicker-to-Thinner

II. INTERFERENCE
Part 1. Wave Interference
Part 2. Principle of Superposition

III. STANDING WAVES
Introduction
Part 1. Both Sides Closed
Part 2. One Side Open
ACTIVITY I.

BOUNDARY BEHAVIOR

As a wave travels through a medium, it will often reach the end of the medium and encounter an obstacle or perhaps another medium through which it could travel. The behavior of a wave upon reaching the end of a medium is referred to as boundary behavior.

In this activity you will use a computer simulation to investigate the boundary behavior of waves in four cases:

1. Fixed End Reflection
2. Free End Reflection
3. Change of medium: Thinner to Thicker
4. Change of medium: Thicker to Thinner

CASE 1. FIXED END REFLECTION

A pulse is introduced at the left end of a rope. The pulse travels through the rope toward the right end of the medium. This pulse is called the incident pulse. In this case the end of the rope is securely attached to a lab pole.

1. Predict what will happen to the pulse as it reaches the fixed end. Sketch your prediction:
2. Click on the SIMULATION and select FIXED END REFLECTION. Describe what you observe:

Does the behavior shown in the simulation agree with your prediction?

3. Using Newton’s Third Law explain why the reflected pulse returns inverted.

4. How does the speed of the reflected pulse compare to the speed of the incident pulse?

5. How does the wavelength of the reflected pulse compare to the wavelength of  the incident pulse?

6. You have learned that a wave is an energy transport phenomenon. What characteristic of a wave is directly related to the energy of the wave?

7. What happens to the energy of the incident pulse as it reaches the boundary?  Where does the energy go? Does the energy disappear?
CASE 2. FREE END REFLECTION

What happens if the rope is free to move at its far end? Instead of being securely attached to a lab pole it is now attached to a ring that is loosely fit around the pole. Because the right end of the rope is no longer secured to the pole, the last particle of the rope will be able to move when a disturbance reaches it. This end of the rope is referred to as a free end.

1. Predict what will happen to the pulse as it reaches the free end. Sketch your prediction:
2. STOP the SIMULATION and select FREE END REFLECTION. Describe what you observe:

Does the behavior shown in the simulation agree with your prediction?

3. What will happen if instead of a crest, a trough is incident upon a free end?

4.  How does the speed of the reflected pulse compare to the speed of the incident pulse?
CASE 3. THINNER TO THICKER

Let's consider a thin rope attached to a thick rope, with each rope held at opposite ends by students. Suppose that the student holding the end of the thin rope introduces a pulse that will travel from the less dense medium toward the boundary with a denser medium (thick rope).

1. Predict what will happen to the pulse as moves from the less dense medium to the denser medium. Sketch your prediction:
2. STOP the SIMULATION and select THINNER TO THICKER. Describe what you observe:

Does the behavior shown in the simulation agree with your prediction?

3. How does the speed of the reflected pulse compare to the speed of the transmitted pulse? Explain.

4. How does the frequency of the reflected pulse compare to the frequency of the transmitted pulse? Explain.

5. How does the wavelength of the reflected pulse compare to the wavelength of the transmitted pulse? Explain.

6. How does the amplitude of the reflected pulse compare to the amplitude of the transmitted pulse? Explain.
CASE 4. THICKER TO THINNER

Now let's consider a thick rope attached to a thin rope, with the incident pulse originating in the thick rope.

1. Predict what will happen to the pulse as moves from the denser medium to the less dense medium. Sketch your prediction:
2. STOP the SIMULATION and select THICKER TO THINNER. Describe what you observe:

Does the behavior shown in the simulation agree with your prediction?

3. How does the speed of the reflected pulse compare to the speed of the transmitted pulse? Explain.

4. How does the frequency of the reflected pulse compare to the frequency of the transmitted pulse? Explain.

5. How does the wavelength of the reflected pulse compare to the wavelength of the transmitted pulse? Explain.

6. How does the amplitude of the reflected pulse compare to the amplitude of the transmitted pulse? Explain.

7. How do you explain the fact that transmitted pulses are never inverted?
CONCLUSION

1. Based on your observations of boundary behavior and using complete sentences write your conclusions about the four wave characteristics (speed, wavelength, frequency and amplitude).

2. In which case(s) does a pulse reaching the end of a medium become inverted?

3. A pulse reaching the end of a medium does not become inverted in which case(s)?

GO TO: ACTIVITY II.