13.3 Interference and Superposition. Interference and Superposition Constructive Interference Destructive Interference Standing Waves

Transcription

1 13.3 Interference and Superposition Interference and Superposition Constructive Interference Destructive Interference Standing Waves

2 Interference and Superposition When raindrops fall into still water, they create tiny waves that spread out in all directions away from the drops. What happens when the waves from two different raindrops meet? They interfere with each other.

3 Interference and Superposition If two baseballs are thrown across the same point at the same time, the balls will hit one another and be deflected.

4 Interference and Superposition Waves, however, can pass through one another. Both observers would hear undistorted sound, despite the sound waves crossing.

5 Interference and Superposition Principle of Superposition When two or more waves are simultaneously present at a single point in space, the displacement of the medium at that point is the sum of the displacements due to each individual wave.

6 Interference and Superposition To use the principle of superposition, you must know the displacement (distance above or below the axis) that each wave would cause if it were alone in the medium. Then you must go through the medium point by point and add the displacements due to each wave at that point.

7 Interference and Superposition

8 Interference and Superposition Example The diagram shows two pulses approaching each other in a uniform medium. Diagram the superposition of the two pulses.

9 Interference and Superposition In general, the superposition of two or more waves into a single wave is called interference.

10 Interference and Superposition Constructive Interference occurs when crest are aligned with crests and troughs with troughs. We say the waves are in phase with each other.

11 Destructive Interference and Superposition Destructive Interference When two or more pulses with displacements in opposite directions interact, the effect is known as destructive interference. Destructive interference occurs when crests are aligned with troughs. We can say the waves are out of phase. The resulting displacements negate each other. Once the pulses have passed by each other, they continue along their original path in their original shape, as if they had never met.

12 Destructive Interference and Superposition Destructive Interference

13 Destructive Interference and Superposition Superposition of two opposite direction wave pulses

14 Constructive Interference Interference and Superposition

15 Destructive Interference Interference and Superposition

16 Interference and Superposition The two waves are represented by red and by orange. At each point, the net displacement of the medium is found by adding the red displacement and the orange displacement. The blue wave is the resulting wave due to superposition.

17 Constructive Interference and Superposition

18 Destructive Interference and Superposition

19 Interference and Superposition Example #1 Two wave pulses on a string approach each other at speeds of 1 m/s. How does the string look at t = 3 s?

20 Interference and Superposition Example #2 Two wave pulses on a string approach each other at speeds of 1 m/s. How does the string look at t = 3 s?

21 Interference and Superposition Example #3 Two waves on a string are moving toward each other. A picture at t = 0 s appears as follows: How does the string appear at t = 2 s?

22 Standing Waves Waves that are trapped and cannot travel in either direction are called standing waves. Individual points on a string oscillate up and down, but the wave itself does not travel. It is called a standing wave because the crests and troughs stand in place as it oscillates.

23 Nodes In a standing wave pattern, there are some points that never move. These points are called nodes and are spaced λ/2 apart.

24 Antinodes Antinodes are halfway between the nodes, where the particles in the medium oscillate with maximum displacement.

25 Nodes and Antinodes At the nodes, the displacement of the two waves cancel one another by destructive interference. The particles in the medium at a node have no motion.

26 Nodes and Antinodes At the antinodes, the two waves have equal magnitude and the same sign, so constructive interference at these points give a displacement twice that of the individual waves. The intensity is maximum at points of constructive interference and zero at points of destructive interference.

27 Nodes and Antinodes Example #4 What is the wavelength of this standing wave? a m b. 0.5 m c. 1.0 m d. 2.0 m e. Standing waves don t have a wavelength.

28 Nodes and Antinodes Example #5 Which of the following types of interference will occur when the pulses in the figure above meet? a. No interference b. Total interference c. Destructive interference d. Constructive interference

29 Nodes and Antinodes Example #6 Which of the following types of interference will occur when the pulses in the figure above meet? a. No interference b. Total interference c. Destructive interference d. Constructive interference

30 Nodes and Antinodes Example #7 How many nodes and antinodes are shown in the standing wave? a. one-third node and one antinode b. three nodes and two antinodes c. two nodes and three antinodes d. one node and two antinodes

31 Nodes and Antinodes Example #8 How many nodes and antinodes are shown in the standing wave? a. five nodes and four antinodes b. four nodes and three antinodes c. four nodes and four antinodes d. three nodes and five antinodes

32 Assessment Assessment #1 Both box waves are traveling a distance of 1 square per second. Draw the superimposed wave after 2 seconds, 4 seconds and 6 seconds

33 Assessment Assessment #1 Both box waves are traveling a distance of 1 square per second. Draw the superimposed wave after 2 seconds, 4 seconds and 6 seconds

34 Assessment Assessment #2 These unusually shaped wave pulses are heading towards each other in a medium whose wave speed is one grid unit per second. Draw the resulting shape of the medium one, two, three, and four seconds later.

35 Assessment Assessment #2 These unusually shaped wave pulses are heading towards each other in a medium whose wave speed is one grid unit per second. Draw the resulting shape of the medium one, two, three, and four seconds later.