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# 4.2

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### 4.2

1. 1. Topic 4.2 Travelling waves
2. 2. Travelling Waves There are two types of waves and pulses that we encounter in the physical world.
3. 3. Transverse  In these waves the source that produces the wave oscillates at right angles to the direction of travel of the wave  It means that the particles of the medium through which the wave travels also oscillates at right angle to the direction of travel of the wave.
4. 4. Direction of travel of the wave Direction of oscillation of the particles Transverse Wave
5. 5. Longitudinal In these waves the source that produces the wave oscillates in the same direction as the direction of travel of the wave It means that the particle of the medium through which the wave travels also oscillates in the same direction as the direction of travel of the wave.
6. 6. Longitudinal Wave Direction of travel of the wave Direction of oscillations of the particles
7. 7. Discrete Pulses and Continuous Waves A single shake of a slinky will send a discrete pulse down it Shake the slinky up and down and a continuous travelling wave travels down it This applies to longitudinal waves too
8. 8. Question: • List 6 types of wave and classify them according to the types you have just learnt.
9. 9. Definitions  The following definitions are given in terms of the particles that make up the medium through which the wave travels.  For the slinky spring a particle would be a single turn of the spring  For the water waves a particle would be a very small part of the water.
10. 10. What is a Wave? A wave is a means by which energy is transferred between two points in a medium without any net transfer of the medium itself.
11. 11. The Medium  The substance or object in which the wave is travelling.  When a wave travels in a medium parts of the medium do not end up at different places  The energy of the source of the wave is carried to different parts of the medium by the wave.
12. 12. Water waves however, can be a bit disconcerting. Waves at sea do not transport water but the tides do. Similarly, a wave on a lake does not transport water but water can actually be blown along by the wind.
13. 13. Displacement (s) is the distance that any particle is away from its equilibrium position at an instance Measured in metres
14. 14. Crest This is a term coined from water waves and refers to the points at the maximum height of the wave. It is the positive displacement from equilibrium
15. 15. Trough  A term coined from water waves referring to the points at the lowest part of the wave. The negative displacement from equilibrium.
16. 16. Compression This is a term used in connection with longitudinal wave and refers to the region where the particles of the medium are "bunched up". High density High pressure
17. 17. Rarefaction A term used in connection with longitudinal waves referring to the regions where the particles are "stretched out". Low density Low pressure
18. 18. Wavelength  () This is the distance along the medium between two successive particles that have the same displacement and the same phase of motion.  Measured in metres
19. 19. Amplitude (A, a) This is the maximum displacement of a particle from its equilibrium position (It is also equal to the maximum displacement of the source that produces the wave). Normally measured in metres
20. 20. Period (T) This is the time that it takes a particle to make one complete oscillation (It also equals the time for the source of the wave to make one complete oscillation). Measured in seconds
21. 21. Frequency  (f) This is the number of oscillations made per second by a particle  (It is also equal to the number of oscillations made per second by the source of the wave)  The SI unit of frequency is the Hertz - Hz. (1 Hz is 1 oscillation per second)  Clearly then, f = 1/T
22. 22. Wave Speed  (v, c) This is the speed with which energy is carried in the medium by the wave.  Measured in m s-1  A very important fact is that wave speed depends only on the nature and properties of the medium
23. 23. Eg • For example, the speed of sound waves in air is typically 330 ms-1 to 350 ms-1 depending on the density of the air and is four times faster in water. Velocity = displacement of crest/time taken • If the time taken is equal to the period T of the wave, the displacement of one crest in this time is equal to  and the equation can be rewritten as: • v = /T • But f = 1/T • so v = f
24. 24. Waves speed table WAVE TYPE MEDIUM SPEED (ms-1) Sound Carbon Dioxide 260 Air 331 Hydrogen 1290 Pure Water 1410 Sea Water 1450 Glass 5500 Light Vacuum 2.997 x 108 Air 2.998 x 108 Glass (crown) 2.0 x 108 Earthquake Crust 3500 (transverse) 8000 (longitudinal) Mantle 6500 (transverse) 11000 (longitudinal)
25. 25. Eg 1 • What will be the time delay in hearing the sound from a brass band for an observer 660 m away? Assume the light arrives instantaneously and the sound travels at 330 ms-1.
26. 26. Solution • v = 330 ms-1 • s = 660 m • t = ? • v = s/t and rearranging; • t = s/v • t = 660/330 • t = 2.0 s
27. 27. Eg 2 • Waves reaching the beach from an offshore storm arrives at 4 s intervals. Calculate the frequency of the waves
28. 28. Solution • T = 4 s T = 1/f • f = ¼ • f = 0.25 Hz
29. 29. Eg 3 • Find the period of a 1 kHz sound wave.
30. 30. Solution • f = 1 kHz = 1000 Hz • T = ? • F = 1/T • rearranging; • T = 1/f • T = 1/1000 • T = 0.001 or 10-3 s.
31. 31. Eg 4 • Calculate the speed of an earthquake wave with a wavelength of 2 km and a frequency of 3 Hz.
32. 32. Solution •  = 2000m • f = 3 Hz • v = ? • v = f • v = 3 x 2000 • v = 6000 m s-1
33. 33. Eg 5 • Given that the speed of sound in air is 330 ms-1, find the wavelength of (a) 20Hz and (b) 20000 Hz sounds.
34. 34. Solution • Part (a) • v = 330 m s-1 • f = 20 Hz •  = ? • v = f •  = 330/20 •  = 16.5 m Part (b) v = 330 m s-1 f = 20 000 Hz  = ? v = f  = 330/20 000  = 0.0165 m  = 1.65 x 10-2 m
35. 35.  A very important property associated with all waves is their so-called periodicity.  Waves in fact are periodic both in time and space and this sometimes makes it difficult to appreciate what actually is going on in wave motion. Periodicity
36. 36. If we drew a diagram that froze time on waves in water We would have an instantaneous snapshot of the whole of the water surface The next diagram shows the periodicity of the wave in space
37. 37. Displacement / Distance displacement distancep
38. 38. The y-axis shows the displacement of the water from its equilibrium position The graph is a displacement- distance graph.
39. 39. We now look at one part of the wave that is labeled p and "unfreeze" time The next diagram shows how the position of p varies with time This illustrates the periodicity of the wave in time
40. 40. Displacement / Time displacement of point p from equilibrium position time
41. 41. The y-axis now shows the displacement of the point p from equilibrium The graph is a displacement-time graph.
42. 42. The space diagram and the time diagram are both identical in shape If we mentally combine them we have the whole wave moving both in space and time.
43. 43. And for Longitudinal Waves? For the longitudinal wave in the slinky spring the displacement- distance graph actually shows the displacement of the individual turns of the spring from their equilibrium position as a function of distance along the spring.
44. 44. However It could equally show how the density of turns of the spring varies with length along the spring.
45. 45. The displacement-time graph shows the displacement of one turn of the spring from its equilibrium positions as a function of time.
46. 46. Wavelength again! Wavelength will therefore be equal to the distance between successive crests and successive troughs.
47. 47. rarefactions wavelength
48. 48. Sound Waves A longitudinal wave in a slinky spring is analogous to a sound wave in which each turn of the spring represents an air molecule.
49. 49. Interpreting Graphs - 1 displacement distance crest trough amplitude crest wavelength amplitude wavelength
50. 50. Interpreting Graphs - 2 displacement time amplitude period period
51. 51. Deriving v = f  Imagine a wave with velocity v Being produced from a source of frequency f In 1 second the 1st wavefront would have travelled a distance of f  As speed = distance / time v = f  / 1  v = f 
52. 52. 2 Important Points 1. The frequency of a wave depends only on the source producing the wave  It will therefore not change if the wave enters a different medium or the properties of the medium change
53. 53. 2. The Speed of waves only depends on the nature and the properties of the medium  Water waves do travel faster in deeper water  Light travels slower in more optically dense material
54. 54. The EM Spectrum Itself Short Long  High fLow f VISIBLERadio Waves Micro Waves Infra red Gamma rays Ultra Violet X rays
55. 55. Wavelengths of Regions (m) • Gamma Rays <10-12 • X-rays 10-10 • Ultraviolet 10-8 • Violet 7.5 x 10-7 > Visible > Red 4.3 x 10-7 • Infrared 10-5 • Microwaves 10-2 • Radio and TV > 103
56. 56. The Different Regions In the context of wave motion, common properties of all parts of the electromagnetic spectrum are  all transverse waves  all travel at the speed of light in vacuo (3.0 x 108 ms-1)  all can travel in a vacuum
57. 57. Sources of Regions  Gamma – certain radioactive material’s nuclei  X-rays – by firing an electron stream at a tungsten metal target in a highly evacuated tube.  Ultraviolet – the Sun, ultraviolet lamp  Visible – hot bodies  Infrared – the Sun (heat), hot bodies  Microwaves – Ovens, communication systems  Radio and TV – transmitter stations, Azteca TV