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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 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
Nexrad
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
Reflection
Fixed End› Inverted› 180o change in phase
Free End› Erect› In Phase
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
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
Superposition
Coherent Sources› Same frequency› In phase
Nodes – complete destructive interference
Antinodes – max constructive interference
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
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
Standing Waves
Nodes – points of zero displacementAntinodes – points of maximum displacement
Node
Antinode
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
Practice Problems
IB text (green)› P.294 ex 11.1(a)
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
Boundary Conditions & Resonance
Resonant standing waves: harmonics› 1st harmonic: fundamental
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
Boundary Conditions & Resonance
Laws of Strings› Law of Lengths f = l’
f’ l› Law of Diameters f = d’
f’ d› Law of Tensions f = √F
f’ √F’› Law of densities f = √D’
f’ √D
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 = 5/4 λ
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 = 3/2 λ
Practice Problems
IB text (green)› P.297 ex 11.1(b)
Walker Text (blue)› P.472 #57-59, 60, 63-65, 68