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9.3 Interference of Waves in 2-Dimensions

9.3 Interference of Waves in 2-Dimensions. Interference. When a wave crest meets a wave trough – destructive interference. Standing Waves. Recall – in a standing wave , points of continuous destructive interference are called NODES. Single Point Source. Point sources make circular waves.

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9.3 Interference of Waves in 2-Dimensions

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  1. 9.3 Interference of Waves in 2-Dimensions

  2. Interference • When a wave crest meets a wave trough – destructive interference

  3. Standing Waves • Recall – in a standing wave, points of continuous destructive interference are called NODES

  4. Single Point Source • Point sources make circular waves

  5. Qualitative Analysis - 2 Point Interference • When a wave crest meets a trough, they cancel = destructive interference • No wave action

  6. http://www.falstad.com/ripple/

  7. Two-Point Source Interference Pattern

  8. Two-Point Source Interference Pattern

  9. Two-Point Source Interference Pattern • Nodal lines numbered 1, 2, 3, …n • Equal distance between all nodal lines = Δx

  10. Quantitative Analysis of 2 Point Interference • S1 and S2 are point sources • P1 is a point on nodal line # 1 • It was found by experiment that |P1S1 - P1S2|=1/2

  11. What would we expect for a point P3 on the 3rd nodal line?

  12. And if we keep doing it we will find that Path difference is always 1/2 if the sources operate in phase. The general formula for path difference becomes: n = the nodal line number starting at 1

  13. Deriving Formula with Values that are easier to measure…

  14. Derivation continued… • If we move Pn far away compared to the distance between the sources. • We end up with a right angle triangle • Therefore AS1 = d sin • sin = 1 give max # of nodal lines

  15. Derivation continued… • Yet  isn’t easy to measure… • ….Almost there…

  16. Derivation continued… • xn = distance from right bisector (B to Pn) • L = distance from centre to node • Similar triangles • (ΔBPd similar to ΔAS1S2) • sin  = xn/L

  17. Derivation continued… Remember: xn is measured from the right bisector to the nodal line

  18. Derivation continued…

  19. Derivation continued…

  20. Derivation continued… Δx=distance between nodal lines (m) L = perpendicular distance from slits to screen (m) d=distance between slits (m) λ=wavelength (m)

  21. Maximum number of nodal lines Maximum value for sin  = 1.0 d (1) = (n-1/2) λ)

  22. Example 1 A 2 point sourcex (same frequency) generate a a point on the 2nd nodal line such that PS1 = 12.3 cm PS2 = 15.5 cm Determine the frequency and the λ of the waves.

  23. Example 2 In a ripple tank the λ of the waves is 2.00 m. Two openings are 3.5 m apart. The end of the tank is 4.00 m beyond the openings. Where along the far wall of the tank is there little/no wave action?

  24. Text Questions • Review example p. 473 into notes • 9.3 p. 459 #1-3 • 9.5 p. 473 #1-8 (2-pt interference) • 9.6 p. 478 #5,6

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