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