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WAVES

WAVES. Wave Motion. Lesson Objectives. By the end of this lesson, you will be able to: State the different types of waves and the difference between them Describe the diffraction of light Explain how to work out the speed of wave propagation. WAVES.

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WAVES

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  1. WAVES Wave Motion

  2. Lesson Objectives By the end of this lesson, you will be able to: • State the different types of waves and the difference between them • Describe the diffraction of light • Explain how to work out the speed of wave propagation

  3. WAVES • Waves transfer energy & information but without transferring matter • The energy is transferred by oscillations in the material which the wave is travelling though

  4. CLASSIFYING WAVES • Mechanical Waves Waves that pass though a material are vibrations of that material eg. Sound waves, seismic waves, strings 2) Electromagnetic Waves Vibrating electrical or magnetic fields through space (no material needed) eg electromagnetic spectrum

  5. C E C E C E TYPES OF WAVES 1. Longitudinal Waves Direction of Travel • Oscillations occur parallel to direction of travel • Sound waves – a vibrating surface in contact with air. • The surface pushes air molecules away which push adjacent air molecules which push adjacent air molecules which push adjacent air molecules which push adjacent air molecules which push adjacent air molecules which push adjacent air molecules which push adjacent air molecules which push adjacent air molecules which push adjacent air molecules which push adjacent air molecules which push adjacent air molecules which push adjacent air molecules which push adjacent air molecules which push adjacent air molecules which push adjacent air molecules which push adjacent air molecules……. Compression (C) Expansion (E)

  6. TYPES OF WAVES 2. Transverse Wave Direction of Travel • Oscillations at right angles (90o) perpendicular to direction of travel • Electromagnetic waves – radiowaves, X-rays, microwaves, visible light etc • Waves on a string or wire – plucking a guitar string

  7. POLARISATION • Can only polarise transverse waves

  8. SEISMIC WAVES • When an earthquake occurs, a majority of the energy is transferred as wave energy and transmitted over long distances. • Classified in 2 types • P primary or push waves • S secondary or shake/shear waves LONGITUDINAL TRANSVERSE

  9. Parts of a Wave Wavelength Peak Amplitude A Trough x 1 complete wave

  10. Key Terms • Displacement (s) – the distance from the equilibrium position • Wavelength (l)– the distance between identical points in a wave train • Amplitude (A) – maximum displacement of a particle (peak or trough max.)

  11. Key Terms • Period (T) – the time taken for 1 complete wave to pass a point • Frequency (f)– number of cycles per second. Measured in Hertz (Hz).

  12. Amplitude and Frequency Low amplitude, low frequency: Low amplitude, high frequency: High amplitude, low frequency: High amplitude, high frequency:

  13. D S T WAVE SPEED • We know the relationship between distance, speed and time. • Speed = Distance / Time • Therefore… Wave Speed = Wavelength / Period V = λ / T But we know that T = 1/f So we can substitute….

  14. The Wave Equation V  f relates the speed of the wave to its frequency and wavelength Wave speed (v) = frequency (f) x wavelength () m/s Hz m

  15. Some example wave equation questions • The speed of sound is 330m/s (in air). When Cuthbert hears this sound his ear vibrates 660 times a second. What was the wavelength of the sound? • a) Purple light has a wavelength of around 6x10-7m. If its frequency is 5x1014 Hz. What is the speed of light? • b) Red light travels at the same speed. Work out its frequency if its wavelength is about 4x10-7m.

  16. TSUNAMI a) A typical tsunami has a wavelength of 300km and a period of 30 mins. What speed does it travel at? b) Brighton is 2800km from La Palma – how long do we have to evacuate before it hits?

  17. WAVE PROPERTIES 1. Reflection Waves will bounce off a surface under certain conditions eg the surface must be shiny for electromagnetic waves Reflective surface Incident Ray Reflected Ray

  18. WAVE PROPERTIES Angle of Incidence Normal Angle of Reflection Angle of Incidence = Angle of Reflection

  19. WAVE PROPERTIES 2. Refraction Waves cross a boundary causing a change in speed and consequently wavelength Depends on the refractive index of different substances Normal Glass Block Air Normal

  20. WAVE PROPERTIES 3. Diffraction • Occurs when waves pass through a gap or around an object of roughly the same size or smaller than their wavelength. • Large gap - the middle parts of the waves go straight through the gap, with a slight curving at the edges of the waves. • Small gap - if the gap is smaller than the wavelength of the waves, the waves fan out in circles.

  21. INTERFERENCE 1. Constructive Interference - when the crests (or troughs) of two waves coincide, they combine to create an amplified wave. The two waves are in phase with each other – there is zero phase difference between them.

  22. INTERFERENCE 2. Destructive Interference - where the crests of one wave are aligned with the troughs of another, they cancel each other out. The waves are out of phase (or in antiphase) with each other – they are half a cycle different from each other.

  23. (Φ) PHASE DIFFERENCE • Measured in radians (rads). • Why? • There is a strong relationship between circular motion and sinusoidal motion. 2π rads = 360° π rads = 180° One wave cycle = 2π rads Angle of one rotation = 2π rads

  24. (Φ) PHASE DIFFERENCE Two waves π/2 radians out of phase

  25. Lesson Objectives By the end of this lesson, you will be able to: • State the different types of waves and the difference between them • Describe the diffraction of light • Explain how to work out the speed of wave propagation GOOD WORK PUNY HUMANS!

  26. Transverse Standing Waves

  27. Standing Waves • One end of a string is attached to a fixed point. • The other end is vibrated up and down. • The standing wave is formed. • Nodes – No movement • Antinodes – most movement

  28. Why they happen • The wave travels along the string until it hits the other end • The wave reflects off the other end and travels in the opposite direction, but upside down • The returning wave hits the vibrating end and reflects again (this side the wave is right side up) • Unless the timing is just right the reflecting wave and the new wave will not coincide • When they do coincide, the wave add due to constructive interference • When they don’t coincide; destructive interference occurs

  29. Harmonics • When you vibrate the string faster, you can get standing waves with more nodes and antinodes • Standing waves are named by number of antinodes • 1 antinode  1st harmonic (fundamental freq) • 2 antinodes  2nd harmonic (1st overtone) • 3 antinodes  3rd harmonic (2nd overtone)

  30. Harmonics • f1 = fundamental frequency (1st harmonic) • f2= 2f1 (2nd harmonic) • f3= 3f1 (3rd harmonic) • Harmonics Example • If the fundamental is 440 Hz (concert A) • 2nd harmonic = 2(440 Hz) = 880 Hz (High A) • 3rd harmonic = 3(440 Hz) = 1320 Hz (really high A)

  31. Equation to Find fn • To find the fundamental frequencies and harmonics of a string fixed at both ends • Where • fn = frequency of the nth harmonic • n = integer (harmonic #) • v = speed of wave • L = length of string

  32. Single Slit Diffraction

  33. Reminder: What is Diffraction? • Bending and spreading of a wave into a region behind an obstruction • Examples: waves passing through openingsor around corners • Effects depend on how wide the opening is relative to wave length • Wide opening: little wave spreading • Narrow opening: wave fans out, changes shape

  34. Diffraction: Why does it occur? According to Huygens’ principle, each point on a wavefront serves as a source of the next wavefront After passing through an aperture, there will be locations where the wavelets interfere constructively and destructively http://id.mind.net/~zona/mstm/physics/waves/propagation/huygens3.html With light, this will result in bright and dark fringes

  35. How single slit pattern is achieved • Using regular uncollimated (incoherent) light: • Lens 1 produces parallel wave fronts passing through slit (coherent light) • Definition: Coherent light has constant phase difference between sources of individual waves • Lens 2 focuses pattern on screen • Alternative: use a laser as the source

  36. Intensity of central fringe is much greater than the rest Width of central maximum is twice that of the others Intensity of central fringe is much greater than the rest

  37. Intensity of central fringe is much greater than the rest Width of central maximum is twice that of the others

  38. Circular Aperture Diffraction Pattern Central maximum is much brighter and wider than the rest This pattern is called an Airy disk That’s all, folks!

  39. Derivation of Single Slit Diffraction Equation: the Setup First dark fringe L

  40. Single Slit Diffraction Applets What happens to fringe width when you change wavelength, slit width, and distance to screen? • http://www.walter-fendt.de/ph14e/singleslit.htm • http://surendranath.tripod.com/Applets/Optics/Slits/SingleSlit/SnglSltApplet.html • http://lectureonline.cl.msu.edu/~mmp/kap27/Gary-Diffraction/app.htm

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