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Topic 4 Oscillations and Waves

Topic 4 Oscillations and Waves. Waves. Waves can transfer energy and information without a net motion of the medium through which they travel. They involve vibrations (oscillations) of some sort. Wave fronts. Wave fronts highlight the part of a wave that is moving together.

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Topic 4 Oscillations and Waves

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  1. Topic 4 Oscillations and Waves

  2. Waves Waves can transfer energy and information without a net motion of the medium through which they travel. They involve vibrations (oscillations) of some sort.

  3. Wave fronts Wave fronts highlight the part of a wave that is moving together. = wavefront Ripples formed by a stone falling in water

  4. Rays Rays highlight the direction of energy transfer.

  5. Transverse waves The oscillations are perpendicular to the direction of energy transfer. Direction of energy transfer oscillation

  6. Transverse waves peak trough

  7. Transverse waves • Water ripples • Light • On a rope/slinky • Earthquake

  8. Longitudinal waves The oscillations are parallel to the direction of energy transfer. Direction of energy transfer oscillation

  9. Longitudianl waves compression rarefraction

  10. Longitudinal waves • Sound • Slinky • Earthquake

  11. Displacement - x This measures the change that has taken place as a result of a wave passing a particular point. Zero displacement refers to the average position. = displacement

  12. Amplitude - A The maximum displacement from the mean position. amplitude

  13. Period - T The time taken (in seconds) for one complete oscillation. It is also the time taken for a complete wave to pass a given point. One complete wave

  14. Frequency - f The number of oscillations in one second. Measured in Hertz (s-1) 50 Hz = 50 vibrations/waves/oscillations in one second.

  15. Wavelength - λ The shortest distance between points that are in phase (points moving together or “in step”). wavelength

  16. Wave speed - v The speed at which the wave fronts pass a stationary observer. 330 m.s-1

  17. Period and frequency Period and frequency are reciprocals of each other f = 1/T T = 1/f

  18. The Wave Equation The time taken for one complete oscillation is the period T. In this time, the wave will have moved one wavelength λ. The speed of the wave therefore is distance/time v =λ/T = fλ

  19. displacement cm Time s 0.1 0.2 0.3 0.4 -1 -2 Displacement/time graph This looks at the movement of one point of the wave over a period of time IMPORTANT NOTE: This wave could be either transverse or longitudnal 1 PERIOD

  20. Displacement/distance graph This is a “snapshot” of the wave at a particular moment IMPORTANT NOTE: This wave could also be either transverse or longitudnal displacement cm 1 WAVELENGTH Distance cm 0.4 0.8 1.2 1.6 -1 -2

  21. Wave intensity This is defined as the amount of energy per unit time flowing through unit area It is normally measured in W.m-2

  22. Wave intensity For example, imagine a window with an area of 1m2. If one joule of light energy flows through that window every second we say the light intensity is 1 W.m-2.

  23. Intensity and amplitude The intensity of a wave is proportional to the square of its amplitude I α a2 (or I = ka2)

  24. Intensity and amplitude This means if you double the amplitude of a wave, its intensityquadruples! I = ka2 If amplitude = 2a, new intensity = k(2a)2 new intensity = 4ka2

  25. Electromagnetic spectrum λ ≈ 700 - 420 nm λ ≈ 10-4 - 10-6 m λ ≈ 10-7 - 10-8 m λ ≈ 10-9 - 10-11 m λ ≈ 10-2 - 10-3 m λ ≈ 10-1 - 103 m λ ≈ 10-12 - 10-14 m

  26. What do they all have in common? • They can travel in a vacuum • They travel at 3 x 108m.s-1 in a vacuum (the speed of light) • They are transverse • They are electromagnetic waves (electric and magnetic fields at right angles to each oscillating perpendicularly to the direction of energy transfer)

  27. Refraction When a wave changes speed (normally when entering another medium) it may refract (change direction)

  28. Snell’s law speed in substance 1 sinθ1 speed in substance 2 sinθ2 =

  29. Snell’s law In the case of light only, we usually define a quantity called the index of refraction for a given medium as n = c cm where c is the speed of light in a vacuum and cm is the speed of light in the medium c vacuum cm

  30. Snell’s law Thus for two different media sinθ1/sinθ2 = c1/c2 = n2/n1

  31. Refraction – a few notes The wavelength changes, the speed changes, but the frequency stays the same

  32. Diffraction Waves spread as they pass an obstacle or through an opening

  33. Diffraction Diffraction is most when the opening or obstacle is similar in size to the wavelength of the wave

  34. Diffraction Diffraction is most when the opening or obstacle is similar in size to the wavelength of the wave

  35. Principle of superposition When two or more waves meet, the resultant displacement is the sum of the individual displacements

  36. Constructive and destructive interference When two waves of the same frequency superimpose, we can get constructive interference or destructive interference. + = = +

  37. If we pass a wave through a pair of slits, an interference pattern is produced

  38. Path difference Whether there is constructive or destructive interference observed at a particular point depends on the path difference of the two waves

  39. Constructiveinterference if path difference is a whole number of wavelengths antinode

  40. Destructive interference if path difference is a half number of wavelengths node

  41. Phase difference • is the time difference or phase angle by which one wave/oscillation leads or lags another. 180° or π radians

  42. Phase difference • is the time difference or phase angle by which one wave/oscillation leads or lags another. 90° or π/2 radians

  43. Simple harmonic motion (SHM) • periodic motion in which the restoring force is proportional and in the opposite direction to the displacement

  44. displacement Time Graph of motion Amplitude x0 Period T x = x0sinωt where ω = 2π/T = 2πf = (angular frequency in rad.s-1)

  45. When x = x0 at t = 0 Amplitude x0 Period T x = x0cosωt displacement Time where ω = 2π/T = 2πf = (angular frequency in rad.s-1)

  46. displacement Time When x = 0 at t = 0 x = x0sinωt v = v0cosωt Amplitude x0 Period T where ω = 2π/T = 2πf = (angular frequency in rad.s-1)

  47. When x = x0 at t = 0 x = x0cosωt v = -v0sinωt Amplitude x0 Period T displacement Time where ω = 2π/T = 2πf = (angular frequency in rad.s-1)

  48. To summarise! • When x = 0 at t = 0 x = x0sinωtand v = v0cosωt • When x = x0 at t = 0 x = x0cosωt andv = -v0sinωt It can also be shown thatv = ±ω√(x02 – x2) and a = -ω2x where ω = 2π/T = 2πf = (angular frequency in rad.s-1)

  49. Maximum velocity? • When x = 0 • At this point the acceleration is zero (no resultant force at the equilibrium position).

  50. Maximum acceleration? • When x = +/– x0 • Here the velocity is zero

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