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STANDING WAVES

STANDING WAVES. Nodes. Antinodes. The distance between adjacent antinodes is λ /2. The distance between adjacent nodes is λ /2. The distance between a node and an adjacent antinode is λ /4. FIXED ENDS. fundamental/1 st harmonic. 2nd harmonic. Normal modes. 3rd harmonic.

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STANDING WAVES

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  1. STANDING WAVES

  2. Nodes

  3. Antinodes

  4. The distance between adjacent antinodes is λ/2. The distance between adjacent nodes is λ/2. The distance between a node and an adjacent antinode is λ/4.

  5. FIXED ENDS fundamental/1st harmonic 2nd harmonic Normal modes 3rd harmonic 4th harmonic

  6. STANDING WAVES IN AIR COLUMNS Open at both ends:

  7. Closed at one end:

  8. Fixed at both ends Open at both ends Fixed at one end – open at the other

  9. RESONANCE An oscillating system is in resonance with some driving force whenever the frequency of the driving force matches one of the natural frequencies of the system; the system responds with a large A.

  10. Phase velocity, Group velocity and Dispersion How might a pulse change shape if the phase velocity is not constant, but depends on frequency?

  11. Phase velocity

  12. e.g., Refractive Index n

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