Chapter 1: Waves

1. Chapter 1: Waves 1.3 Analysing Refraction of Waves

2. 1.3 Analysing Refraction of Waves Any type of wave can be refracted, which means a change of direction. Refraction occurs when the speed of a wave changes, as it moves from one medium to another. We shall look at the refraction of water waves, light waves and sound waves.

3. Refraction of Plane Water Waves 1 Water waves undergo refraction (bending) when they are slow down. Refraction is accompanied by a change in speed and wavelength of the waves.

4. Refraction of Plane Water Waves 2 Water waves travel faster (with higher velocity, v) on the surface of deep water than they do on shallow water. Thus, if water waves are passing from deep water into shallow water, they will slow down. This decrease in speed will also be accompanied by a decrease in wavelength. The change in speed of the wave causes refraction. Figure 1.31

5. Refraction of Plane Water Waves 3 After refraction, the wave has the same frequency, but a different speed, wavelength and direction.

6. Refraction of Plane Water Waves 4 When a water wave transmitted from deer water into shallow water, the wave is refracted towards the normal.

7. Refraction of Plane Water Waves Conversely, the wave is refracted away from the normal when the water wave transmitted from shallow water into deep water. The effects of refraction of water waves are shown in Figures 1.32 (a) and (b).

8. Refraction of Plane Water Waves Experiment 1.4: To investigate the refraction of water waves What are the effects on the direction of propagation of a water wave passing over Perspex plates of different shapes?

9. Refraction of Plane Water Waves Hypothesis Refraction occurs and the direction of propagation is influenced by the shapes of the Perspex plates.

10. Refraction of Plane Water Waves Variables: (a) Manipulated : Shapes of Perspex plates (b)Responding : Wavelength and direction of propagation of the water wave (c) Fixed : Frequency

11. Refraction of Plane Water Waves Apparatus/Materials Ripple tank, wooden bar, perspex plates of different shapes, mechanical stroboscope and white paper.

12. Refraction of Plane Water Waves Procedure 1 A ripple tank is set up as shown in Figure 1.30.

13. Refraction of Plane Water Waves Procedure 2 The tank is filled with water and the legs of the tank are adjusted until the depth of the water in the tank is uniform.

14. Refraction of Plane Water Waves Procedure 3 A Perspex plate in the shape of a trapezium, as shown in Figure 1.31, is immersed in the centre of the tank to create an area of shallow water in the tank.

15. Refraction of Plane Water Waves Procedure 4 The dipper with the wooden bar attached is switched on to produce plane waves.

16. Refraction of Plane Water Waves Procedure 5 The directions of the water waves in the areas of deep and shallow water are observed with a stroboscope.

17. Refraction of Plane Water Waves Procedure 6 Steps 3 to 5 are repeated with the orientation of the trapezium plate changed so that the wave is incident at an acute angle on a side of the plate as shown in Figure 1.32.

18. Refraction of Plane Water Waves Procedure 7 Steps 3 to 5 are repeated using Perspex plates in the shapes of a triangle, convex lens and concave lens.

19. Refraction of Plane Water Waves Procedure 7 Steps 3 to 5 are repeated using Perspex plates in the shapes of a triangle, convex lens and concave lens.

20. Refraction of Plane Water Waves Procedure 7 Steps 3 to 5 are repeated using Perspex plates in the shapes of a triangle, convex lens and concave lens.

21. Refraction of Plane Water Waves Procedure 7 Steps 3 to 5 are repeated using Perspex plates in the shapes of a triangle, convex lens and concave lens.

22. Refraction of Plane Water Waves Procedure 7 Steps 3 to 5 are repeated using Perspex plates in the shapes of a triangle, convex lens and concave lens.

23. Refraction of Plane Water Waves Discussion 1 Refraction occurs when a water wave passes from one area to another area with a different depth of water.

24. Refraction of Plane Water Waves Discussion 2 If the wave strikes the perspex plate at an angle of incidence of 0�, the direction of propagation of the wave remains unchanged. The water wave is not refracted, i.e. the angle of refraction is zero.

25. Refraction of Plane Water Waves Discussion 3 If the wave strikes the Perspex plate at a certain angle of incidence, the water wave is refracted.

26. Refraction of Plane Water Waves Discussion 4 The water wave is refracted towards the normal the wave travels to a shallower area, and vice versa.

27. Refraction of Plane Water Waves Conclusion The direction of propagation of a wave changes if the angle of incidence of the wave is not zero. The shape, of the refracted wave depends on the shape of the area of shallow water over which the wave is passing.

28. Refraction of Plane Water Waves Example 7: Figure 1.35 shows water ripples in two areas of water with different depths. The observation is made with a stroboscope with 3 slits. The frequency of the stroboscope is 4 rotations per second

29. Refraction of Plane Water Waves Calculate (a) the frequency of the dipper,

30. Refraction of Plane Water Waves Solution (a) Frequency of dipper = Number of slits x Frequency of stroboscope = n x p = 3 x 4 = 12Hz

31. Refraction of Plane Water Waves Calculate (b) the wavelength in the deep area and in the shallow area,

32. Refraction of Plane Water Waves Solution (b) Area of deep water: Wavelength , Area of shallow water: Wavelength

33. Refraction of Plane Water Waves Calculate (c) the speeds of the waves in the two areas.

34. Refraction of Plane Water Waves Solution (c) Area of deep water: Speed Area of shallow water: Speed = 9.6 cm s-1

35. Refraction of Plane Water Waves Example 8 A plane wave has a wavelength of 2 cm and a velocity of 8 cm s-1 as it moves over the surface of shallow water. When the plane wave moves into an area of greater depth, its velocity becomes 12 cm s-1. What is (a) the wavelength (b) the frequency of the wave in the area of greater depth?

36. Refraction of Plane Water Waves Solution (a) Area of shallow water: v1=8 cm s-1 and ?1=2cm Area of deeper water: v2=12 cm s-1 and ?2=? For refraction, frequency, f = remains the same. Substituting in the relationship:

37. Refraction of Plane Water Waves Example 8 A plane wave has a wavelength of 2 cm and a velocity of 8 cm s-1 as it moves over the surface of shallow water. When the plane wave moves into an area of greater depth, its velocity becomes 12 cm s-1. What is (b) the frequency of the wave in the area of greater depth?

38. Refraction of Plane Water Waves Solution (b) Frequency of wave, f = = 4 Hz The frequency of the wave is the same in all the areas.

39. Refraction of light 1 A swimming pool seems much shallower than it actually is; a spoon appears bent when part of it is in water and a boy's legs look shorter when immersed in a pool. All these effects are due to the refraction of light.

40. Refraction of light 2 Figure 1.37 shows that a light ray is bent or refracted when passing from air to the glass.

41. Refraction of light 3 When a ray propagates from one medium to an optically denser medium, the ray refracts towards the normal. Conversely, a ray propagating from one medium to an optically less dense medium is refracted away from the normal.

42. Refraction of light 4 The speed of the light decreases as it propagates in the glass block, causing it to alter the direction of propagation. Since the incidence ray and the refracted ray are from the same source (ray box), the frequency remain the same. Hence, the wavelength of the ray in the glass is shorter than the ray in the air.

43. Refraction of Sound Waves 1 The sound of a moving train at a distance is clearer at night than that in the day time. This is due to the effects of the refraction of sound waves.

44. Refraction of Sound Waves 2 At night-time, the layers of air close to the ground are cooler than the layers further from the ground.

45. Refraction of Sound Waves 3 Sound travels at a slower speed in cold air. As a result, the sound waves are refracted in front path of a curve (due to total internal reflection) towards the ground instead of disappearing into the upper layers of the air.

46. Refraction of Sound Waves Experiment 1.5 To investigate the refraction of sound waves What happens to a sound wave as it passes through a balloon filled with carbon dioxide?

47. Refraction of Sound Waves Hypothesis A sound wave of greater amplitude is produced after it passes through the balloon filled with carbon dioxide.

48. Refraction of Sound Waves Variables (a) Manipulated : Balloon filled with carbon dioxide (b) Responding : Amplitude of the sound wave displayed on the screen of the cathode-ray oscilloscope (c) Fixed : Frequency of the sound wave

49. Refraction of Sound Waves Apparatus Audio signal generator, loudspeaker, balloon fillet with carbon dioxide, microphone and cathode-ray oscilloscope.

50. Refraction of Sound Waves Procedure 1 The apparatus is set up as shown in Figure 1.39. Figure 1.39

51. Refraction of Sound Waves Procedure 2 The experiment is started without the balloon.

52. Refraction of Sound Waves Procedure 3 The audio signal generator and the cathode-ray oscilloscope are switched on. The wave form displayed on the screen of the oscilloscope is observed and drawn.

53. Refraction of Sound Waves Procedure 4 A balloon filled with carbon dioxide is placed between the audio signal generator and the oscilloscope. 5 The wave form displayed on the screen is observed and drawn.

54. Refraction of Sound Waves Results

55. Refraction of Sound Waves Results The wave form displayed on the oscilloscope shows that the amplitude is larger when the balloon is placed between the audio signal generator and the oscilloscope. The larger amplitude indicates that a louder sound is received by the microphone.

56. Refraction of Sound Waves Discussion A sound wave is refracted towards the normal when the wave passes from the air to the carbon dioxide in the balloon. This is because carbon dioxide is denser than air and the speed of sound in carbon dioxide is reduced.

57. Refraction of Sound Waves Discussion When the sound wave emerges from the balloon, the wave is refracted away from the normal. The balloon acts as a biconvex lens which converge the sound waves to the microphone.

58. Refraction of Sound Waves Conclusion Sound waves are refracted when they travel from one medium to another of different density. The sound waves are refracted away from the normal after passing through the balloon filled with carbon dioxide. The result is a sound wave with larger amplitude. The hypothesis is valid.