1. Waves Topic 4.5 Wave Properties

2. Wave Behaviour v Reflection in one dimension

3. This diagram shows a pulse travelling along a string

4. This diagram shows the pulse after it has been reflected

5. Notice v The pulse keeps its shape v It is inverted v It has undergone a 180 o phase change, or  change in phase

6. Fixed vs Free-end Reflection v The inversion is because the instant the pulse hits the fixed end, the rope attempts to move the fixed end upwards v It exerts an upwards force on the fixed end v By Newton’s third law, the fixed end will exert an equal but opposite force on the rope v This means that a disturbance will be created in the rope which is “downwards” and will start moving to the left

7. v If the end of the rope is not fixed but free to move the situation is different v Most of the pulse would carry on in the same direction, some would be reflected but the reflected pulse is in the same phase as the original pulse v There is a change of direction, but no inversion here Fixed vs Free-end Reflection

8. Wave Behaviour v Reflection in two dimensions

9. Reflection Wavefronts incident upon a boundary… Incident waves Reflected waves

10. Normal Angle of incidence Angle of reflection =

11. The Law for Reflection The angle of incidence is equal to the angle of reflection -keep in mind that angles are measured with respect to the normal at point of contact Also - The incident ray, the reflected ray and the normal lie on the same plane Use this rule for any ray or wave diagram involving reflection from any surface

12. For circular waves hitting a flat reflector, the reflected waves appear to come from a source, which is the same distance behind the reflector as the real source is in front of it Also a line joining these 2 sources is perpendicular to the reflecting surface

13. O I

14. If a plane wave is incident on a circular reflector then the waves are reflected so that they –Converge on a focus if the surface is concave –Appear to come from a focus if the surface is convex

15. Incident wavefronts Reflected wavefronts (semi circles)

16. Incident wavefronts Reflected wavefronts

17. Wave Behaviour v Refraction

18. The speed of a wave depends only on the nature and properties of the medium through which it travels. Refraction is the change of direction of travel of a wave resulting from a change in speed of the wave when it enters the other medium at an angle other than right angles.

19. In a ripple tank this is achieved by using a flat piece of plastic, giving two regions of different depth As the wave passes over the plastic it enters shallow water and slows down. Remember: v = f If v decreases and f is constant (the source hasn’t changed) must also decrease, so the waves get closer together

20. If the waves enter the shallow area at an angle then a change in direction occurs. Shallow water

21. This is because the bottom of the wavefront as drawn, hits the shallow water first so it slows, and hence travels less distance in the same time as the rest of the wavefront at the faster speed travel a larger distance!

22. Deep water If the waves enter the deep area at an angle then a change in direction occurs

23. This is because the top of the wavefront hits the deep water first so it speeds up, and hence travels more distance in the same time as the rest of the wavefront at the slower speed travel a smaller distance!

24. Refraction for light Partial reflection Incident ray Refracted ray Partial reflection

25. Snell’s Law Snell discovered that for any two media Sin  1 / Sin  2 = constant The constant is…the ratio of the wave velocity in the two media v 1 / v 2 Where  1 is the angle of incidence in the 1st medium, v 1 is the velocity in that medium And  2 is the angle of refraction in the second medium, v 2 is the velocity

26. Therefore Or… n 1 sin  1 = n 2 sin  2 Where n is the index of refraction of the media For light and optics… n vacuum = 1 (also taken as the value in air)

27. This law enable us to define a property of a given optical medium by measuring  1 and  2 when medium 1 is a vacuum The constant is then the property of medium 2 alone and it is called the refractive index (n). We usually write n = (Sin i) / (Sin r) n is also a ratio of the speeds in the 2 mediums i.e. n = c vacuum / v medium

28. Diffraction Diffraction is the spreading out of a wave as it passes an obstacle or through an aperture (an opening) When the wavelength is small compared to the aperture the amount of diffraction is minimal. When the wavelength is comparable to the size of the opening then diffraction effects are significant.

32. Diffraction also takes place when a wave moves passed an obstacle If the wavelength is much smaller than the obstacle, little diffraction takes place If the wavelength is comparable to the obstacle size, then diffraction is significant

34. Huygens’ Principle Christian Huygens' idea was to consider every single point on the wavefront of the wave as the source of a new wave disturbance. In other words a point on the wavefront would emit a spherical “wavelet” or secondary wave, of same velocity and wavelength as the original wave.

35. Therefore as a wave goes through a gap or passed an obstacle the wavelets at the edges spread out the wave energy. Huygens’ construction can be used to predict the shapes of the wave fronts. Huygens’ Principle

37. The new wavefront would then be the surface that is tangent to all the forward wavelets from each point on the old wavefront. We can easily see that a plane wavefront moving undisturbed forward easily obeys this construction.

38. The Principle of Linear Superposition Pulses and waves (unlike particles) pass through each other unaffected and when they cross the total displacement of the medium is the vector sum of the individual displacements due to each pulse at that point.

39. Interference Most of the time in Physics we are dealing with pulses or waves with the same amplitude. If these cross in a certain way we will get full constructive interference, here the resultant wave is twice the amplitude of each of the other 2 + =

40. If the pulses are 180 o (  ) out of phase then the net resultant of the string will be zero. This is called complete destructive interference. + =