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Waves

Waves. (part 2). Doppler Effect. Depends on relative motion of source and detector Closer = decr wavelength Incr pitch Blue shift Farther = incr wavelength Decr pitch Red shift. Doppler Effect. EM waves do not require a medium Speed of light can be different for different observers

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Waves

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  1. Waves (part 2)

  2. Doppler Effect • Depends on relative motion of source and detector • Closer = decr wavelength • Incr pitch • Blue shift • Farther = incr wavelength • Decr pitch • Red shift

  3. Doppler Effect • EM waves do not require a medium • Speed of light can be different for different observers • One Doppler effect-it depends on the relative speed between the observer and the source • Doppler radar-EM waves are sent out • Change in frequency of the reflected beam relative to the outgoing beam measures speed of clouds and precipitation that reflected the beam

  4. Nexrad

  5. Practice Problems • IB text (green) • P.299-300 ex 11.2(a) & (b) • Walker Text (blue) • P.471 # 34, 35, 38, 42, 44, 45, 46, 84

  6. Reflection • Fixed End • Inverted • 180o change in phase • Free End • Erect • In Phase

  7. Reflection, Refraction, & Transmission • Waves at a discontinuity, or boundary between different media • Part of wave is reflected. • Part of wave is transmitted into the new medium. • The “heavier”, or “more rigid”, or “denser” the second section: the more is reflected & less transmitted

  8. Superposition • Principle of Superposition • The net effect of two causes is found by adding the individual effects of each cause. • Crest + Crest = one larger crest • Constructive Interference • Crest + Trough = zero displacement • Destructive Interference • Interference need not be complete

  9. Superposition • Coherent Sources • Same frequency • In phase • Nodes – complete destructive interference • Antinodes – max constructive interference

  10. Practice Problems • IB text (green) • P.124 ex 4.5(b) & P.442 ex 18.3 • Walker Text (blue) • PP.471-472 #47-49, 51, 53, 55

  11. Standing Waves • Two waves moving through a medium simultaneously will interfere • Speed depends on medium • If frequency is correct, interference will result in a waveform which appears to stand still

  12. Standing Waves Node Antinode Nodes – points of zero displacement Antinodes – points of maximum displacement

  13. Nature & Production of Standing Waves • Usually produced by reflected wave interfering with incident wave • From rigid surface • Nodal points @ source & point of reflection • Standing wave does not propagate energy

  14. Practice Problems • IB text (green) • P.294 ex 11.1(a)

  15. Boundary Conditions & Resonance • Resonance • An oscillatory system is driven by a driving force that has a frequency equal to the natural frequency of oscillation of the system • Can be useful or harmful

  16. Boundary Conditions & Resonance • Resonant standing waves: harmonics • 1st harmonic: fundamental

  17. Boundary Conditions & Resonance • Strings • Fixed end reflection = phase change • 1st harmonic: L = ½ λ • 2nd harmonic: L = λ • 3rd harmonic: L = ¾ λ • 4th harmonic: L = 2λ

  18. Boundary Conditions & Resonance • Laws of Strings • Law of Lengths f = l’ f’ l • Law of Diameters f = d’ f’ d • Law of Tensionsf = √F f’ √F’ • Law of densities f = √D’ f’ √D

  19. Boundary Conditions & Resonance • Columns of air (pipes) • Closed end reflection • phase change • Node at the end • Only odd harmonics are present • 1st harmonic: L = ¼ λ • 3rd harmonic: L = ¾ λ • 5th harmonic: L = 5/4λ

  20. Boundary Conditions & Resonance • Columns of air (pipes) • Open end reflection • No phase change • Antinode at the end • All harmonics are present • 1st harmonic: L = ½ λ • 2nd harmonic: L = λ • 3rd harmonic: L = 3/2λ

  21. Practice Problems • IB text (green) • P.297 ex 11.1(b) • Walker Text (blue) • P.472 #57-59, 60, 63-65, 68

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