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Understanding Waves Interference: Constructive and Destructive Effects

yoshe avatar
yoshe
24 diapositives · 402 Views · Sep 03, 2014

This lecture focuses on the fundamental concepts of wave interference in physics, specifically constructive and destructive interference. We explore how waves from two speakers interact, the path-length differences, and the resulting interference effects. Key experiments demonstrate how frequency changes can affect sound wave patterns. The discussion also touches upon light waves, diffraction, and the principles of thin film interference, illustrating how these phenomena reflect the wave nature of light. Perfect for students wanting to deepen their understanding of wave behavior.

#understanding waves interference: constructive and destructive effects #understanding waves interference: constructive and destructive effects ppt #powerpoint #presentation
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  1. From last time… • Waves Interference Please pick up pack of color sheets Phy208 Lecture 2

  2. constructive interference,loud tone destructive interferencequit tone Interference of 2 speakers cresttrough Phy208 Lecture 2

  3. A little more detail Path-length difference  = (Path 2) - (Path 1) = 0 Same distance, same phase Path 1 Path 2 Path 1 Path 2 d Phy208 Lecture 2

  4. Other angles? Path-length difference 0 Interference: Constructive: = Destructive: = Path 1 Path 2   = Extra path length d Phy208 Lecture 2

  5. Question Suppose that the frequency of the sound wave increases by a factor of two. The adjacent maxima are A) Farther apart B) Closer together C) Same D) Need to know speaker spacing Higher frequency, -> shorter wavelength Less path length diff required to make 1 wavelength diff. Phy208 Lecture 2

  6. Question In your room you have two speakers in different corners. At your desk you are exactly 1 meter from each, so that there is no interference. Your roommate moved one of your speakers 0.25 m further away from your desk. At what frequency will you hear destructive interference? • 170 Hz • 340 Hz • 680 Hz • 1000 Hz • 1350 Hz Phy208 Lecture 2

  7. Path 2  Path 1  = Extra path length d Math Analysis Constructive interference:  = 0.347 rad = 19.9˚ Phy208 Lecture 2

  8. with  in radians For small , e.g. Exact value: For small angles… Small angle approximation for constructive interference Approx breaks down for large  Phy208 Lecture 2

  9. Light waves • Light is a wave just like sound. • But can propagate in vacuum • at speed c = 3x108 m/s • Has same wave properties, e.g. • Can also propagate in glass, water, but slower • Speed in medium = v = c/n • n = Index of refraction • Has same superposition / interference properties Phy208 Lecture 2

  10. Interference of light Phy208 Lecture 2

  11. y  L Recording plate Projection on screen • Light wavelength much shorter than sound • Interference fringes much closer together Light beam Foil with two narrow slits Phy208 Lecture 2

  12. Extra path length =  Small-angle approximation  = Extra path length y = position on screen = Phy208 Lecture 2

  13. Bright Fringe separation = Fringe separation & wavelength • For bright fringes: extra path length = m • For dark fringes: extra path length = (m+1/2)  Phy208 Lecture 2

  14. Question A two-slit interference pattern is observed in air (n=1). Then the entire system is immersed in water (n=1.33). The interference fringes are A) 1.33 times closer together B) 1.33 times farther apart C) 2.66 times closer together D) 2.66 times farther apart E) Spacing unchanged Phy208 Lecture 2

  15. Evenly-spaced slits have maxima at same location as two-slits. • Maxima become sharper, more intense • Interference of multiple sources often called diffraction Interference of multiple sources Phy208 Lecture 2

  16. Diffraction gratings • Diffraction grating is pattern of multiple slits. • Very narrow, very closely spaced. • Expect very narrow interference peaks. (15,000 lines/inch)x(1 inch/2.54 cm)x(100 cm/m)=5.9x105/m So a spacing of 1/(5.9x105/m) = 1.7x10-6 m = 1700 nm. 1700 nm Phy208 Lecture 2

  17. Question Suppose white light is shined through a diffraction grating. What would the pattern on the screen look like? A) B) C) D) Phy208 Lecture 2

  18. Diffraction: only one slit, but “wide” • Huygen’s principle: each portion of the slit acts as a source of waves • These sources interfere according to path-length difference. Phy208 Lecture 2

  19. Diffraction minima • Interference-like pattern from a single slit. How wide is wide? Phy208 Lecture 2

  20. General reln: Phase difference • Waves start in phase • Travel different distances (extra path length = ) • No longer in phase when combined (Phase diff ) =/2  =π =  =2π Constructive: =2πm Destuctive: =2π(m+1/2) Phy208 Lecture 2

  21. Thin film interference Black Colors changing with thickness Phy208 Lecture 2

  22. Thin film interference  180˚ (π radians) phase shift • If film is much thinner than wavelength, ~ no phase shift from extra path length • But top reflection has 180˚ phase shift, bottom not • Destructive interference for all wavelengths, film appears black no phase shift air: n=1 n>1 /n t Phy208 Lecture 2

  23. destructive 180˚ phase shiftfrom reflection Thicker parts  • Phase difference comes from • Phase shift from reflection (top) • Phase shift from extra path length • Extra path length for normal incidence = 2t air: n=1 n>1 Extra path length=2t t vac/n air: n=1 Phase difference = Reflection phase shift # wavelengths in extra path length Phy208 Lecture 2

  24. Constructive interference constructive interference destructive interference Phy208 Lecture 2