1. Wave Interference
Chapter 8.3

2. Starter
What is the relationship between the amplitude of a wave and the energy carried through the wave?
When a wave reaches the boundary of a new medium, part of the wave is reflected and part transmitted. What determines the comparative sizes of the reflective and transmitted wave?
A pulse reaches the boundary of a new medium more dense than the one from which it came. Is the reflected pulse erect or inverted?

3. Answers
The bigger the amplitude of the wave, the more energy the wave has.
The type of medium and how different it is. Example: A hard wall vs a soft/padded wall. The hard wall will reflect more of the wave than the soft wall (which will absorb more). If a wave goes from more dense to less dense, the amplitude/energy will be more in the transmitted wave than the reflected wave and vice versa.
Inverted

4. 4) Waves are sent along a spring of fixed length.
a) Can the speed of the waves in the spring be changed? Explain.
b) Can the frequency of a wave in the spring be changed? Explain.
5) You repeatedly dip your finger into a sink full of water to make circular waves. What happens to the wavelength, velocity, and frequency as you move your finger faster?

5. Answers
4) a) No. Since the spring is of fixed length, the medium cannot be changed. Since the speed of waves depends on the medium, the speed cannot be changed.
B) Yes, the frequency of the wave can be changed by producing more or fewer waves each second.
5) Wavelength – decreases, since the waves are being created closer together.
Velocity – stays the same, since the medium has not changed.
Frequency – increases, since you are creating more waves every second

6. What is wave interference?
Objects cannot occupy the same space at the same time.
However, waves can as they are ENERGY (not material).
Wave interference occurs when 2 waves pass through the same region of space at the same time
(copy last bullet)

7. In Phase (copy)
In Phase - Two waves with the same frequency are in phase if their crests and troughs occur at the same time.
Example:

8. Out of Phase (copy)
When two waves with the same frequency are not “in sync” (crest of one wave does not occur when crest of the other wave occurs).
Quick Video of out of phase example

9. In Phase/Out of Phase Example
If I drop two rocks in water and they produce waves with the same frequency, there are some places where the waves arrive in phase. This means that two crests arrive at the same time. The two crests move the water upwards to make a larger wave at that moment in time.
In other places, the waves will arrive out of phase. When a crest arrives from one rock, a trough arrives from the other rock. This time, the effect of the waves cancel each other out.

10. Superposition (copy)
When two waves occupy the same space at the same time, their energies are “added together” temporarily.
These waves do not need to have the same amplitude or frequency.
Note: If it is a crest, think of it as positive. If it is a trough, think of it as negative.

11. Types of Interference (copy)
A) Constructive Interference (in-phase)
When 2 crests arrive at the same time (or 2 troughs) OR at any point where the waves “add” together to make a larger wave (temporary)

12. Constructive Interference

13. Constructive Interference

14. Constructive Interference
Note here that the amplitudes still add together but the values are considered negative. The amplitude still increase but in the negative direction.

15. Types of Interference (copy)
B) Destructive Interference (out of phase)
When 1 crest and 1 trough arrive at the same time and cancel each other out if they are identical in size (temporarily).

16. Destructive Interference

17. Destructive Interference

18. Types of Interference (copy)
Partially destructive
If waves are not identical in size, they will not cancel each other but dampen the wave temporarily.

19. Partially Destructive Interference

20. Constructive Destructive Partially Destructive

21.
Cool example of interference.

22. Quick Quiz
1. Several positions along the medium are labeled with a letter. Categorize each labeled position along the medium as being a position where either constructive or destructive interference (partial included) occurs.

23. Answers Constructive Interference: G, J, M and N
Destructive Interference: H, I, K, L, and O

24. Are waves destroyed with destructive interference?
No!
They are temporarily “changed” when they are in the same place at the same time. This is not permanent.

25. Principle of Superposition (copy)
In the region where the waves overlap, the result and displacement is the algebraic sum of their separate displacements.
NOTE: A crest is positive and a trough is negative!
NOTE: Waves do not change shape or size when they meet. They can pass through each other. However, when they overlap, a different shaped wave emerges temporarily! After the interference they continue their movement in the same direction, with the same amplitude and energy.

26. Example of Superposition (copy)
If one wave has an amplitude of +3cm and the other wave has an amplitude of -6cm, the resultant displacement is …
-3cm.
Examples:

27. Example 2 of Superposition (copy)
If one wave has an amplitude of +3cm and the other wave has an amplitude of +6cm, the resultant displacement is …
+9cm.
See page 355 for diagrams!

28. Superposition of Waves
What will happen when the waves “meet up”?
What will happen after they meet up?

29. Superposition of Waves

30. Questions for You Page 362 – 1, 2
Question 3: What principal tells you this?

31. Answers
1. Constructive interference – amplitude at superposition is 4 cm (2 + 2).
2. Destructive interference - cancel out ( = 0).
3. Principle of Superposition – states that the displacement is the sum of the separate displacements

32. Worksheet

33. Try This Get a cup of water Get a few different tuning forks
Strike the tuning fork. You can’t see the air move.
Put the vibrating tuning fork in the water. What happens?

34. Think about…. When you were a child, did you play “telephone”?
Here’s how it works: Using 2 cups, attach a string from 1 cup to the other.
What happens if you talk in one cup?
Explain why the other person can hear!
The air vibrates the cup, the string, the cup, etc

35. How does a record work?
2nd section

36. Standing Waves
When two pulses with equal but opposite amplitudes meet.
The waves have the same shape, amplitude and wavelength but opposite directions.

37. Node
You can find points in the medium that are completely undisturbed at all times (destructive interference).
A point where disturbances caused by two or more waves result in no displacement.
**MATH 11: On the SA!

38. Antinode
You can find one point that undergoes the greatest displacement.
Point of maximum displacement of two superimposed waves (constructive interference)
Occur at crests and troughs.
Occur halfway between nodes.

39. There are nodes at the end of a rope and antinodes in the middle.
The resulting wave appears to be standing still. This is a standing wave.

40. Page 357

41. Page 357

42. How do we get a standing wave?
Have one vibrating source.
The second wave is actually the reflected wave from the incident wave
Example: Violin strings
Waves move toward the fixed ends of the violin. When they reach the ends, the waves reflect back. There is interference. Standing waves form if nodes occur at the ends of the string/violin. This occurs if the strings are vibrating at the resonance frequency.

43. Animation

44. Questions for You
Page 362
4, 5

45. Answers
4. You would see nodes evenly spaced and antinodes (as crests and troughs at the same time) evenly spaced between the nodes. It is called a standing wave because the nodes are not moving.

46. 5. The nodes are distributed at distances of half the wavelength (as are the antinodes). The antinodes are spaced evenly between these. Nodes are on the equilibrium or sinusoidal axis. Antinodes are found at troughs and crests.
Nodes are caused by destructive interference. Antinodes are caused by constructive interference.

47. Questions for You!
Page 343, questions 3, 4, 6, 7