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# 1.5 Interference of Waves

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• slinky spring demonstrate the superposition of two transverse waves.
• ### 1.5 Interference of Waves

1. 1. 1.5 Interference of waves www.myfunphysicsworld.blogspot.com
2. 2. Learning Outcomesstate the principle of superposition,explain the interference of waves,draw interference patterns,interpret interference patterns, andsolve problems involving www.myfunphysicsworld.blogspot.com
3. 3. Water waves move towards the side of the boatand are reflected backThe incident waves and the reflected waves aresuperposed.Ripples can be seen clearly in areas where thewater is calmprinciple of superposition. www.myfunphysicsworld.blogspot.com
4. 4. Wave interferencePhenomenon when two or morewaves meet while traveling alongthe same medium at the sametime www.myfunphysicsworld.blogspot.com
5. 5. Principle of superposition of wavesTwo mechanical waves superposed (1) produce awave with a higher amplitude (2). www.myfunphysicsworld.blogspot.com
6. 6. Principle of Superposition of waves When two waves superpose, the resulting displacementof the medium at any location is the algebraic sum of the displacements of individual waves. www.myfunphysicsworld.blogspot.com
7. 7. 5cekap here 22feb2011 www.myfunphysicsworld.blogspot.com
8. 8. www.myfunphysicsworld.blogspot.comHow does interference occur???A crest superposes a A through superposes acrest, the displacement trough, the displacementof the resultant wave is of the resultant wave isthe sum of the the sum of thedisplacement of displacementindividual waves atevery point. the displacement is negative.
9. 9. 2 type of Interference1. Constructive interference occurs when a crest meets a crest and when a trough meets a trough.2. Destructive interference occurs crests meets/superposes with troughs. www.myfunphysicsworld.blogspot.com
10. 10. Constructive interferenceInterference that occurs at any location alongthe medium where the two interfering waveshave a displacement in the same direction occurs when a crest meets a crest //when a trough meets a trough. www.myfunphysicsworld.blogspot.com
11. 11. Destructive interferenceInterference that occurs at any locationalong the medium where the two interferingwaves have a displacement in the oppositedirection www.myfunphysicsworld.blogspot.com
12. 12. Destructive interferenceA crest that superposes a trough wave arrivesexactly out of phase,the crest of a wave meets the trough of the other.They cancel each other and the water is calm, www.myfunphysicsworld.blogspot.com
13. 13. Destructive interference of two waveswith different amplitude www.myfunphysicsworld.blogspot.com
14. 14. www.myfunphysicsworld.blogspot.com
15. 15. Interference by 2 coherent sources www.myfunphysicsworld.blogspot.com
16. 16. Coherent sourcesThe waves from coherent sources havethe same frequency (f), same wavelength(λ) and constant phase difference.The difference in the distances of a pointfrom the two sources is called pathdifference.Two waves with a path difference of 2λ. www.myfunphysicsworld.blogspot.com
17. 17. Node Nodal lines Antinodal lines Antinodewww.myfunphysicsworld.blogspot.com
18. 18. Path difference of Z from S1 and S2 =|x1-x2| www.myfunphysicsworld.blogspot.com
19. 19. 1. For constructive interference (point Z), path difference=nλ2. For destructive interference (point W), Path difference= (n+1/2) λ www.myfunphysicsworld.blogspot.com
20. 20. Factors affecting the interference Young’s Formula www.myfunphysicsworld.blogspot.com
21. 21. Young’s formulaWavelengthof the waves,a = the distance between two coherentsources of wave,x = the separation between two adjacent nodalor antinodal linesD = the perpendicular distance between wavessource to the position where x is measured. www.myfunphysicsworld.blogspot.com
22. 22. 1.When a & D constant, λ increase, x? x increase2.When D & λ constant, a increase, x? x decrease3. When a & λ constant, D increase, x? x increase www.myfunphysicsworld.blogspot.com
23. 23. www.myfunphysicsworld.blogspot.com
24. 24. Example 1.2In a ripple tank experiment, two water superpose and formInterference patterns.The distance between the two vibrating sources is 3.0 cm.The separation between two adjacent nodal line is 5.4 cm,at a distance of 10.5 cm from the two sources.Calculate the wavelength of the water waves produced 5.4 cm 10.5 cm ? 3.0 cm Young’s Formula www.myfunphysicsworld.blogspot.com
25. 25. In a ripple tank experiment, two water wavessuperpose and form interference patterns. Thedistance between the two vibrating sources is 3.0cm. The separation between two adjacent nodal lineis 5.4 cm, at a distance of 10.5 cm from the twosources.Calculate the wavelengthof the water waves produced. www.myfunphysicsworld.blogspot.com
26. 26. Young’s Double-slit experiment www.myfunphysicsworld.blogspot.com
27. 27. A laser beam after passing through a double slitForming an interference pattern consisting alternatedark & bright fringes www.myfunphysicsworld.blogspot.com
28. 28. Young’s Double-slit experiment (pg 27) Bright fringe bri gh Dark fringe t Bright fringe Dark fringe Bright fringe Dark fringe Bright fringe Dark fringeMonochromatic source, propagate perpendicularlytowards a double-slit form interference fringes. www.myfunphysicsworld.blogspot.com
29. 29. Bright fringe Dark fringe www.myfunphysicsworld.blogspot.com
30. 30. Exp on Interference of sound wave www.myfunphysicsworld.blogspot.com
31. 31. What do the blue & red lines represent? www.myfunphysicsworld.blogspot.com
32. 32. Homework:1. QR 1.5 page 28 (#1-3) 2. Page 46, Section B. www.myfunphysicsworld.blogspot.com
33. 33. 1. QR 1.5 page 281.What is the meaning of two coherent waves? Two sets of waves that have same wavelength, frequency and constant phase different. www.myfunphysicsworld.blogspot.com
34. 34. 2. Figure shows A and B are two sources of wave from the motor engine of two boats. The frequencies of these two sources of wave are 5 Hz and 10 Hz. (a) What happens to the amplitude of wave at the point of superposition when (i) the crests of the waves from A and B meet, (ii) the crests of the wave from source A meet the troughs of the wave from source B? (b) Are the waves A and B coherent? Explain.FigureTwo boats approaches each other. www.myfunphysicsworld.blogspot.com
35. 35. 2.(a) (i) The amplitude will be twice (ii) The amplitude will be zero(b) No, different frequency www.myfunphysicsworld.blogspot.com
36. 36. 3.Figure shows S1 and S2 which are two spherical sources attached to the vibration bar of a ripple tank. The two sources are separated at a distance of 5.0 cm. (a) Are the waves produced by S1 and S2 coherent? Explain. (b) State the phenomena produced at the position P, R and T. www.myfunphysicsworld.blogspot.com
37. 37. 3(a) Yes, they come from the same source (Same f, λ and phase difference)(a) R and P : Constructive Interference T : destructive Interference www.myfunphysicsworld.blogspot.com
38. 38. HomeworkPage 46, Section B.*Both semicircular waves must have samesize of λ.(c) From the diagram, measure D and x.(d) Calculate λ. www.myfunphysicsworld.blogspot.com
39. 39. www.myfunphysicsworld.blogspot.com
40. 40. The destructive interference of two waves with different amplitude. A crest with amplitude of a unit meet a trough with amplitude of -2a units the resulting displacement amplitude is -a unitwww.myfunphysicsworld.blogspot.com
41. 41. Destructive interferencea crest of one wavepropagates from the leftsuperposed on anothertrough coming from theright.The resulting wave willcancel each other.There is no resultingdisturbance in themedium. www.myfunphysicsworld.blogspot.com
42. 42. interference of 2 sources of lines.The dotted red lines join places where the wavesarrive there in phaseRed lines called antinodal linesjoin places of constructive interference. www.myfunphysicsworld.blogspot.com
43. 43. blue lines where calm water is formedwaves arrive there exactly out of phase.Blue lines are called nodal lines.join the places of destructive interference www.myfunphysicsworld.blogspot.com
44. 44. The distance of Z from the S1 is x1,the distance of Z from the S2 is x2.The path difference of Z from S and is x2-x1.consructive interference (S), the path difference = nλ.destructive interference (W), the path difference = (n +1/2) λn is an integer. www.myfunphysicsworld.blogspot.com
45. 45. Draw two adjacent antinodal lines on both the photographs.a. How does the separation of the antinodal lines differs?b. If the separations of the two sources of vibrations are a1, and a2, what is the reIationship between a1 and a2 to that of the separations of the antinodal lines?c. How do you measure the wavelengths of the two sources of wave?d. Are the waves produced by the two sources of vibration coherent? Explain. www.myfunphysicsworld.blogspot.com
46. 46. when the sources are closer to each other, the nodaland antinodal lines of the interference patterndecrease in number and are more widely spaced.when the separation of the two dippers decrease, thenodal (and antinodal) lines increase in number andalso become closely spaced.If the separation is further increased, the nodal linesbecome so close together until they are hardlynoticeable.As the wavelength of the waves increases, theseparations of the nodal and the antinodal lines willincrease.The number of the antinodal or nodal lines willdecrease. www.myfunphysicsworld.blogspot.com