6 WAVE BEHAVIOUR Basic wave properties

1. 6 WAVE BEHAVIOURBasic wave properties • Review key wave properties • Explain the meaning of the terms phase, phasor and superposition Starter: Q1. Define the following wave terms: wavelength, frequency, amplitude, period, wave speed. Q2. What is the wavelength of radio waves whose period is 9 ns?

3. Frequency is the number of wave cycles per second Period is the time it takes for one complete oscillation Add on the labels: peak, trough, wavelength, amplitude. Think about what frequency, wave speed, period are

4. Waves have phase Waves in phase Waves out of phase Waves with 90° phase difference

5. Using phasors to describe the phase of a wave 1. A phasor is a rotating arrow that represents the phase of wave without having to draw it out. 2. The higher the frequency of the wave the more rapidly the phasor rotates. 3. The larger the amplitude of the wave the longer the phasor. 4. Different representations of the waves describe exactly the same thing.

7. Adding waves with different phases The principle of superposition says that the resultant amplitude of two waves in the same point is the sum of their individual amplitudes at this point. Phasors can also be used to describe what the resultant wave looks like when two waves superimpose. See page 126

11. Superposition phenomena • Observe and explain some phenomena involving wave superposition • Explain how superposition is used in some practical situations Starter: Q1. If two waves are to constructively interfere, what must be true about their frequency, wavelength and phase? Q2. Sound waves from two speakers driven from the same signal generator arrive at a point, 180o out of phase. What must be true about the path lengths taken by the two wave trains?

12. Path difference: the difference in distance (path) two waves have travelled to reach the receiver Maxima occur where the path difference is a whole number of wavelengths e.g. 1, 2, 3….. (the waves arrive in phase) Minima occur when the path difference is an odd number of half wavelength e.g. 0.5, 1.5, 2.5…. (the waves arrive out of phase) Now try questions 30S

13. In order for stable superposition effects it is necessary to have waves that are coherent Coherence means waves that have constant phase difference If incoherent waves are used then the superposition effects will vary such as the beats observed with two slightly different frequencies. All waves from the same source are inherently coherent

14. Radar guns • If the path to the car and back is a whole number of wavelengths then there is a maxima. • If it is a whole number of half wavelengths then it is a minima. When the car moves towards the detector maxima and minima are recorded sequentially. The frequency the signal varies at can be used to calculate the speed the car is approaching

15. Now try questions 70S When you have finished; read textbook page 127 on oils and soap colours and take down enough notes that you can explain the phenomenon to your partner

16. Look at the pretty bubbles! Can you explain, in terms of wave superposition, why you see a spectrum of colours in the surface of the bubble?

19. Can you work out the superimposed wave from these phasors? + = + =

20. Standing waves • Describe how standing (stationary) waves are created by superposition of travelling waves • Describe and explain the pattern of nodes and antinodes formed by standing waves on strings and in pipes

23. Standing waves in air Investigate and explain standing waves patterns in air columns Starter: Write down two similarities and two differences between transverse waves and longitudinal waves

25. Apply your understanding of standing waves Q1. What is the frequency of the second harmonic note produced by an organ pipe 1.3 m long, which is closed at one end? (Speed of sound in air = 340 ms-1.) Q2. Can you explain, in terms of standing waves, why a flute produces higher pitch notes than a clarinet?

26. Generate questions from these answers • Half a wavelength • A node at each end • A node at one end and an antinode at the other • The harmonics follow the pattern f, 2f, 3f, 4f,..... • The speed of sound will increase and the frequency will increase but the wavelength will remain the same

27. Fiendish problem Ignore the fact that all of the members of the orchestra would be asphyxiated! • Suppose while an orchestra was playing you pumped out all of the air from the concert hall and replaced it with helium, through which sound travels much faster than through air. What would happen to the pitch of the different instruments? Would all types be affected equally? Hints: The pitch is an indication of the frequency. All of the sounds are produced by standing waves, either on strings under tension or in columns of air.

28. The nature of light • Explain Romer’s method for estimating the speed of light • Discuss differences between wave and particle models of light • Review evidence for light behaving as either wave or particle

29. What evidence from every day life is there to suggest that the speed of light is much higher than the speed of sound? • Sketch diagrams to illustrate reflection, refraction, diffraction and interference. • Which of the 4 wave phenomena above can be explained ONLY by a wave model of light? Why? • “Looking at the night sky is looking back in time.” Explain this statement.

30. Light interference • Observe light interference and explain it in terms of superposition • Measure the wavelength of light of a laser using Young’s slits Starter: Use the transparencies to create 2-source interference patterns. What happens to the spacing between the regions of constructive and destructive interference when the sources are moved apart?

31. Can you describe the interference pattern of sound and water waves? RIPPLE Tank If we were to try the same experiment with light. What problems might we face?

33. Young’s slits experiment R x Q d P L Screen

35. Bright fringes occur when this length is a whole number of wavelengths sin q = nl/d nl = dsinq

36. R x Q q d P L sin q can also be calculated by looking at the big triangle that the fringes create tanq = x/L sinq= x/L Screen

37. Predicting where bright fringes will be: sinq = nl/d sinq= x/L x/L = nl/d x = nLl/d l = xd/L

38. Write down an estimation of the uncertainty in the measurements of x, d and L Look at the equations we have derived and make a prediction about what effect changing the slit spacing have on this experiment.

39. The diffraction grating • Observe and explain transmission and reflection diffraction grating effects • Measure a laser wavelength using a transmission grating Starter: Use the equation nλ= d sin θ to predict the effect on a 2-slit interference fringe pattern of changing to slits that are further apart. Verify using the transparencies.

41. d is the spacing between adjacent slits on the grating Gratings d The first maximum occurs when the length indicated is equal to l

42. Gratings The angle is increased until the length indicated becomes equal to 2l d The order of the maxima corresponds to the number of l difference in the path length Note that by the same argument it can be shown that: n l=d sinq

43. Now calculate the wavelength of the maxima. Can you explain why the maxima are more spread out than when we used a double slit? Diffraction gratings can be used in: Separating different frequencies of light for analysis Observing the spectrum of stars Selecting particular wavelength for use Now try Qs 3-6 p144

44. Reflection grating

45. Starter: Draw a diagram to show how plane waves diffract when they pass through an aperture: • when the aperture is much larger than the wavelength of the waves • when the aperture is comparable in size to the wavelength of the wave

46. Single aperture diffraction • Observe and explain single slit diffraction • Explain some practical consequences in astronomy and every day life

47. DiffractionPatterns • 1. How does the diffraction spreading depend on the wavelength of light? • 2. Carefully adjust the width of the slit. How does the diffraction spreading depend upon slit width? .

50. Beam width Link • Note that W is really referring to half the beam width • sin q =W/L = l/d • so for small angles: • beam angle in radianq = l/d