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Exploring Wave Superposition and Interference Phenomena

Delve into the concepts of wave superposition, interference, and reflection with animations and demonstrations to understand how waves add up, interfer, and interact based on frequency, amplitude, and phase differences. Explore standing waves in various configurations and harmonic modes.

elizabethmorris
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Exploring Wave Superposition and Interference Phenomena

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  1. Wave superposition, interference, and reflection

  2. Adding waves: superposition • When two waves are incident on the same place at the same time, their amplitudes can usually just be added. • In the next few slides we will look at some special cases: (both with two waves at the same frequency and with the same amplitude) • same frequency and amplitude • superposition at a point in space • same direction, but different phase • opposite directions

  3. Adding waves • In most simple systems, the amplitude of two waves that cross or overlap can just be added together.

  4. Adding two equal amplitude waves at a point

  5. For which phase difference  is the superposition amplitude a maximum? • =0 • =/2 • = 

  6. For which phase difference  is the superposition amplitude a minimum? • =0 • =/2 • = 

  7. Adding two waves that have the same frequency and direction, but different phase • What happens when the phase difference is 0? • What happens when the phase difference is /2? • What happens when the phase difference is ?

  8. Constructive interference when =0. • Destructive interference when =. Link to animation of two sine waves adding in and out of phase (Kettering)

  9. What happens when a wave is incident on an immovable object? • It reflects, travelling in the opposite direction and upside down. (Now watch patiently while your instructor plays with the demonstration.)

  10. Same frequency, opposite directions • What happens when kx is 0? • What happens when kx is /2? • What happens when kx is ? Link to animation of two sine waves traveling in opposite directions

  11. Standing waves • Interfering waves traveling in opposite directions can produce fixed points called nodes. • y1= ym sin(kx – wt) • y2= ym sin(kx + wt) v=w/k • yT = y1 + y2 = 2ym cos(wt) sin(kx) • yT=0 when kx = 0, p, 2p... • yT(t)=maximum when kx = p/2, 3p/2, 5p/2 ...

  12. Fundamental mode (1st harmonic, n = 1) 2nd harmonic, n = 2 Standing waves - ends fixed • Amplitude will resonate when an integer number of half-wavelengths fit in the opening. • Example: violin 5th harmonic, n = 5

  13. Both Ends Fixed

  14. Fundamental mode (1st harmonic), n = 1 l=4L/n, n odd 3rd harmonic, n = 3 9th harmonic, n = 9 Standing waves - one end free • Free end will be an anti-nodeat resonance. • Demo: spring (slinky) with one end free.

  15. One End Open (e.g. Organ Pipe)

  16. Fundamental mode (1st harmonic), n = 1 l=2L/n 5th harmonic, n = 5 2nd harmonic, n = 2 Standing waves - both ends free Example: wind instrument

  17. Both Ends Open (e.g. Organ Pipe)

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