Apply superposition principle Differentiate between constructive and destructive inference.

1. 12.4 Wave interactions • Apply superposition principle • Differentiate between constructive and destructive inference. • Predict when a reflect wave will be inverted. • Predict whether specific traveling waves will produce a standing wave. • Identify nodes and antinodes of a standing wave.

2. Wave Interference • Aphenomenon which occurs when two WAVES MEETwhile traveling along the same medium. • The interference of waves causes the medium to take on a shape which results from the SUPERPOSITIONof the two individual waves. The two waves meet, produce a net resulting shape of the medium, and then CONTINUEon doing what they were doing before the interference.

3. Constructive interference • Occurs where the two interfering waves have a displacement in the same direction. The result is a LARGER AMPLITUDE. MAXIMUMconstructive interference occurs when the waves are in PHASE(phase difference is 0o or 360o) and crest superposes on crest or trough on trough. 1 unit 2 units The point of maximum displacement of a medium when two waves are interacting is called an ANTI-NODE. -1 unit -2 units

4. Destructive interference • Occurs where the two interfering waves have a displacement in the opposite direction. Destructive interferences result a SMALLER amplitude. • Maximum destructive interference occurs when two waves of equal frequency and amplitude whose phase difference is 180o or ½ λ meet at a point. Maximum destructive interference results in the formation of NODES. Which are regions ofZERO displacement of the medium

5. Constructive Destructive

6. principle of superposition • When two waves interfere, the resulting displacement of the medium at any location is the ALGEBRAIC SUM of the displacements of the individual waves at that same location. +2 -2 0 -1

7. Example #1 Determine type of interference of each section as constructive or destructive. III I II

8. Example #2 Apply superposition principle to determine result of interference by sketch the resultant wave.

9. CLASS WORK – today’s date • Two waves having the same amplitude and the same frequency pass simultaneously through a uniform medium.  Maximum destructive interference occurs when the phase difference between the two waves is •   0° c.  90° •   180° d. 360° The diagram shows two pulses, each of length, traveling toward each other at equal speed in a rope. Which diagram below best represents the shape of the rope when both pulses are in region AB?  a. c. b. d.

10. Maximum constructive interference between two waves of the same frequency could occur when their phase difference is a. 1λ b. ¼ λ c. ½ λ d. 1 ½ λ • The diagram below represents shallow water waves of wavelength λ passing through two small openings, A and B, in a barrier. How much longer is the length of path AP than the length of path BP? • a. 1λ b. 2λ c. 3λ d. 4λ

11. The diagram below represents shallow water waves of constant wavelength passing through two small openings, A and B, in a barrier. Compared to the length of path BP, the length of path AP is how many wavelength longer? • Which statement best describes the interference at point P? • It is constructive, and causes a longer wavelength. • It is constructive, and causes an increase in amplitude. • It is destructive, and causes a shorter wavelength. • It is destructive, and causes a decrease in amplitude.

12. The diagram shows two sources, A and B, vibrating in phase in the same uniform medium and producing circular wave fronts.  Which phenomenon occurs at point P? • destructive interference • constructive interference • reflection • refraction

13. 8. Determine the interference pattern

14. Reflection of a Pulse Fixed Point Floating Point before before after after The reflected pulse is INVERTED. This inversion can be explained by Newton's third law of action-reaction. The reflected pulse have the SAME DIRECTIONas the incident pulse.

15. Changing Mediums Fast  Slow Slow  Fast less dense denser denser less dense before before after after

16. Characteristics of transmitted pulse and reflected pulse • The wave speed is always GREATEST IN THE LEASTdense rope. • The wavelength is always GREATEST IN THE LEAST DENSErope. • The frequency of a wave is NOT ALTEREDby crossing a boundary. • The reflected pulse becomesINVERTEDwhen a wave in a less dense rope is heading towards a boundary with a denser rope. • The amplitude of the incident pulse is always greater than the amplitude of the reflected pulse.

17. Example • A pulse moves from a very thick rope into a thin string. Circle the term that makes the statement true. • The transmitted pulse will lose / gain amplitude. • The transmitted pulse will lose / gain speed. • The transmitted pulse will lose / gain energy. • The reflected pulse will / will not come back on the opposite side.

18. Two sources in phase in the same medium crests troughs Constructive: Point A, B are anti-nodes Destructive: Point C, D, E, F are nodes

19. Standing Waves • A WAVE PATTERN what results when two waves of the SAME frequency, wavelength, and amplitude travel in OPPOSITE DIRECTIONSand interfere • A standing wave pattern is formed as the result of the perfectly timed interference of two waves passing through the same medium. A standing wave is NOT actually A WAVE; rather it is the PATTERN.

20. Nodes and anti-nodes in a standing wave Nodes: the points of ZERO displacement of the resultant wave Antinotes: the points of MAXIMUMdisplacement of a medium The distance between two successive nodes is ½ λ standingWaveDiagrams1/StandingWaveDiagrams1.html

21. 1st harmonic • Standing wave patterns are only created within the medium at SPECIFIC FREQUENCIES OF VIBRATION. These frequencies are known as HARMONICS. • ..\..\RealPlayer Downloads\Standing Wave on a String.flv • Standing waves can be created for both transverse and longitudinal waves. • pipe-waves.html 2nd harmonic 3rd harmonic

23. Standing waves in water • Standing waves in water are produced most often by periodic water waves REFLECTING FROM A BARRIER.

24. Example #1 • What is the number of nodes and antinodes in the standing wave shown in the diagram?   8 nodes 7 antinodes

25. Example #2 The diagram represents a wave moving toward the right.                     Which wave shown below could produce a standing wave with the original wave? 1 2 4 3

26. Example #3 • Two waves traveling in the same medium and having the same wavelength (λ) interfere to create a standing wave. What is the distance between two consecutive nodes on this standing wave? • λ • ½ λ • ¼ λ • ¾ λ

27. Class work – today’s date • Sketch a pulse that shows the superposition of the pulse pairs below.

28. A pulse with a height of +0.5 meter encounters a second pulse with a height of +2.3 meters. a. The two pulses interfere: ___________________________ b. The resulting height of the medium when the pulses interfere will be: ______________ m • A pulse with an amplitude of 0.4 meter moves from a thick, heavy cord where its speed is 2.0 meters per second into a much thinner string. The speed and height of the pulse after it is transmitted could be: • Amplitude = 0.5 m; Speed = 1.0 m/s • Amplitude = 0.3 m; Speed = 1.0 m/s • Amplitude = 0.5 m; Speed = 3.0 m/s • Amplitude = 0.3 m; Speed = 3.0 m/s

29. Which of the following is transmitted by a pulse? (1) energy and mass (2) mass only (3) energy only • The energy contained in a pulse is related to its: (1) amplitude and speed (3) width and speed (2) amplitude only (4) speed only • As pulses travel they lose: (1) amplitude and speed (3) width and speed (2) amplitude only (4) speed only • A pulse moves from a very thick rope into a thin string. Circle the term that makes the statement true. (a) The transmitted pulse will lose / gain amplitude. (b) The transmitted pulse will lose / gain speed. (c) The transmitted pulse will lose / gain energy. (d) The reflected pulse will / will not come back on the opposite side.

30. Sketch the superposition of the following sets of pulses.

31. The grid below represents a 10.0 meter long string. • Sketch the standing wave that this string would produce if it were to have SIX nodes. • Draw a circle around each ANTINODE on the string. • Determine the wavelength of this standing wave. _________________m • Assuming that this wave moves at 2.0 meters per second, calculate its frequency and period.

32. Two point sources produce a pattern of overlapping circular waves. The solid lines in the diagram represent wave crests while the dotted lines represent wave troughs. Mark a “C” in the boxes that indicate constructive interference and a “D” in the boxes that indicate destructive interference.

33. Sketch a wave that will completely destructively interfere with the wave shown below. What is the phase difference between these two waves? At the point when the two waves shown below completely overlap, what will the superposition of the two waves look like? Draw a sketch of the wave produced during this interaction.

34. A standing wave is produced as a result of a combination of _______________ and _______________________. The main features of standing waves are: ______________________ at which minimum motion of the medium occurs. _______________________ at which maximum motion of the medium occurs. • Determine the wavelength of the standing wave shown below. Identify one node and one anti-node.

35. A (NODE/ANTINODE) is the result of an alternating phase difference of 0 and 180 degrees between two waves passing through each other. (Circle one) • To produce a standing wave, two waves must: • o be moving in _______________________________ • o have the same: •  _____________________________ •  _____________________________ •  _____________________________

36. The grid below represents a 10 meter long string. • Sketch the standing wave that this string would produce if it were to have SIX nodes. • Draw a circle around each ANTINODE on the string. • Determine the wavelength of this standing wave. _________________m • Assuming that this wave moves at 2.0 meters per second, calculate its frequency and period.