Kinds of waves. Mechanical waves. Electromagnetic waves. Matter waves?

Transcription

1 Waves

2 Waves are Energy

3 Kinds of waves Mechanical waves Electromagnetic waves Matter waves?

4

5 What is a wave? A wave is a form of energy transfer: often through a disturbance in the medium Same sine wave as you get with a pendulum

6 Properties of waves Amplitude Wavelength Frequency Period Medium? Direction

7 f 1 T Inverse Ex 1: find the period of a wave with a frequency of 0.25 Hz T 1 s f Hz 0.25s 1 4 Ex 2: find the frequency of a wave with a period of 5 ms T 1 1 f 200Hz T 0.005s 1 f

8 Ex 1: find the angular velocity of an object with a frequency of 0.25 Hz ω=2πf =2π(0.25Hz) ω= 1.57 rad s 1 Ex 2: find the angular velocity of an object with a period of 5 ms ω=2π/t =2π/0.005s ω=1260rad s 1

9 Start p. 103 #1-2

10 0.35 Lab Prep Pendulum Lab Purpose: to measure g Procedure: refer to text, p. 5 but with the following changes: Observations: Name Date Block Partner Length /m Time (10) /s Period /s Period^

11 What does the graph tell us? Since 2 T 2 l g g 2 4 l 4 2 T slope Find g from your graph, then write a conclusion comparing your result to gravitational field g=9.8 m/s 2

12 Simple Harmonic Motion

13 Ex 3: sketch the graph of motion of the object from example 1 if it started from 7cm above equilibrium position x=7cos(1.5t)

14 Start p. 105 #3-6

15 Ex 4: find the velocity at 2.7s v= -ωx o sin(ωt) v=-11sin(1.57t) v=9.8cm s ⁱ

16 Simple harmonic motion We have angular velocity: ω=2πf and ω=2π/t This gives:

17 Ex 5: find the velocity at 2.7 cm v= 1.57 sqrt(7^2-2.7^2) v=10.1cm s 1

18 Start p. 107 #7-9 Variable Symbol Unit Angular frequency AKA angular velocity Displacement (relative to equilibrium) Amplitude x 0 m Period T s Frequency f Hz s -1 Force F N Time t s x m

19 We can hear wavelength as pitch

20 How does our ear pick up these frequencies?

21 Some snakes can see infrared light

22 Bees can see in UV

23 The mantis shrimp is a delightfully weird beastie. They re multi-coloured, their genus and species names mean mouth-feet and genital-fingers ; they can move each eye independently, they see the world in 11 or 12 primary colours as opposed to our humble three, and now we find that this species can see a world invisible to the rest of us, said Professor White, of the University of Queensland. Mantis shrimps, dubbed thumb splitters by divers because of their vicious claws, have the most complex eyes in the animal kingdom, capable of seeing colors from the ultraviolet to the infrared, as well as detecting other subtle variations in light. They view the world in up to 12 primary colors- four times as many as humans - and can measure six different kinds of light polarization, Swiss and Australian researchers reported.

24 How damp is it?

25 How damp is it? An object undergoing SHM will lose amplitude due to friction, fluid resistance, etc. The amount of damping can be classified as:

26 Start p. 107 #7-9

27 Lab 8.2 p. 155 Gore Text 1. Waves were faster in the smaller slinky 2. Same 3. Amplitude does not affect wave speed 4. Spring tension is proportional to speed 5. Only the disturbance travels 6. The waves reflected inverted (crest reflected as a trough)

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29 The wave equation For a wave with speed v, frequency f and wavelength, we have: v=f Ex 1: find the speed of a water wave with wavelength 2.5 m and frequency 3 Hz

30 Don t forget: Chocolate Lab: use a (pure) chocolate bar, the bigger the better, and a microwave oven to measure the speed of light Bring the chocolate for a Wednesday lab day.

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32 Wave transmission When a wave encounters a different medium, we always find: part of the wave is transmitted part of the wave is reflected The reflected wave will be: upright if the 2nd medium is less dense inverted if the 2nd medium is more dense

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34 We can see wavelength as color

35 For light, we have: c=f EM radiation Ex 1: find the frequency of green light f c m 9 s m Hz

36 Ex 2: find the speed of light if wavelength is measured to be 14 cm c f 0.14( ) m s 1

37 Ex 2: find the frequency of a 6.0 fm gamma ray photon f c m 15 s m Hz

38 Ex 3: find the wavelength of The River f=97.5 MHz v=c c f m 6 c f m s Hz

39 Energy with SHM Total energy is a constant, depending on amplitude x₀ By conservation of energy, this also means:

40 Kinetic energy Ex: find the kinetic energy for a 10 g mass on a spring stretched 13 cm, when it is at a position of -3.5 cm

41 Potential energy can be found from other information, e.g. Gravity or solved from total energy Ex: find the potential energy for a spring stretched 13 cm, when it is at a position of -3.5 cm

42 Lab 8-4 p.160 Tuesday? Exercises P.159 #1-6

43 Lab 8-4 p Do parts 1-4 Lab 8-4 Answer Concluding Questions: #1-2 p. 161 (reflection from straight barrier) #1-2 p. 162 (reflection from parabola) #1-3 p. 163 (diffraction)

44 Wave Action

45 Types of wave action Refraction Diffraction Refl action?

46 Reflection We find the waves are reflected with the same angle

47 Diffraction We find the waves bend around the barrier We get more diffraction with long wavelength, small opening

48 Refraction We can bend waves when they encounter a different medium

49 Start p. 125 #10-12

50 What is resonance? If vibrations match an objects natural oscillation, it resonates Greenhouse gases resonate in the infrared range and absorb those frequencies

51 Interference When waves encounter each other, we have found they pass through When they occupy the same location in space, they interfere The resultant wave is the integer sum of the individual waves at each point

52

53 Wave Interference Draw the resultant of these two waves interfering. The resultant at each point is the integer sum of the magnitudes.

54 Draw the resultant of these two waves interfering. Remember that the resultant at each point is the integer sum of the magnitudes.

55 Constructive vs. destructive interference

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57

58 Start p. 127 #13

59 The Doppler Effect

60 Since the waves move outward in concentric spheres, the wavelength is observed as being equal in all directions. Stationary Source

61 These circles no longer have the same centre. The observer will measure a different wavelength from a different direction Moving Source

62 Light Doppler? Very fast moving objects will even show a Doppler effect with emitted light Blue shift: moving towards us Red shift: moving away This is how we know the universe is expanding!

63 Doppler formula If the source is moving: Ex: find the frequency we hear for a 3000Hz sound from a car moving towards us at 25 m/s

64 Ex: find the frequency we hear for a 3.0 khz sound from a car moving towards us at 25 m/s f f 3200Hz

65 Doppler formula If the observer is moving: Ex: find the frequency we hear for a 250Hz sound if we run away at 13 m/s

66 Ex: find the frequency we hear for a 250Hz sound if we run away at 13 m/s f f 240Hz

67 Doppler formula For light: f f c Ex: find the change in frequency we see for red light if a star moves away at 513,000 m/s

68 c f f c Hz f f c Hz

69 P. 136 q s P. 138 q s Snell labs due Monday

70 Shock Waves?

71 As the source moves faster through the medium, you can see that the wavefronts start piling up in front of the object, e.g. the sound barrier. Approaching the speed of sound the craft encounters the sound waves piled on top of each other. Once the craft breaches the sound barrier, it leaves its sound waves behind. The edges of these waves form a shock wave known as the sonic boom

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73 P. 201 Test Yourself 1-11 odds Labs due now

74 Scattering

75 Speed of Light c

76 Why is light so difficult to measure? Compared to sound (343 m/s) light seems instantaneous Galileo made the first attempt to measure c

77 Why is light so difficult to measure? Roemer (1676) made the first successful measurement, from eclipses of Io ~ km/s

78 More accurate measurements Bradley (1728) stellar aberration ( km/s) Fizeau rotating wheel ( km/s) Foucault rotating mirror ( km/s) Michelson-Morley interferometer km/s

79 Measure the æther wind? Since all waves need a medium, it was believed light moved through a medium called the æther. The Michelson-Morley interferometer was precise enough to measure the æther wind rushing past the Earth

80 Results? They measured the same speed!