Lesson 3: Behavior of Waves

2. Lesson 3: Behavior of Waves • Boundary Behavior • Reflection, Refraction, and Diffraction • Interference of Waves • The Doppler Effect

3. Boundary Behavior • As a wave travels through a medium, it will often reach the end of the medium and encounter an obstacle or perhaps another medium through which it could travel. • An example is a sound wave reflecting off canyon walls and other obstacles to produce an echo. • A sound wave traveling through air within a canyon reflects off the canyon wall and returns to its original source.

4. Boundary Behavior • The behavior of a wave (or pulse) upon reaching the end of a medium is referred to as boundary behavior. • When one medium ends, another medium begins; the interface of the two media is referred to as the boundary and the behavior of a wave at that boundary is described as its boundary behavior.

5. Fixed End Reflection • First consider an elastic rope stretched from end to end with one end securely attached to a pole. • The last particle of the rope will be unable to move when a disturbance reaches it. This end of the rope is referred to as a fixed end.

6. Fixed End Reflection • If a pulse is introduced at the left end of the rope, it will travel through the rope towards the right end of the medium. • This pulse is called the incident pulse since it is incident towards (i.e., approaching) the boundary with the pole..

7. Fixed End Reflection • When the incident pulse reaches the boundary, two things occur: • A portion of the energy carried by the pulse is reflected and returns towards the left end of the rope. The disturbance that returns to the left after bouncing off the pole is known as the reflected pulse. • A portion of the energy carried by the pulse is transmitted to the pole, causing the pole to vibrate.

8. Fixed End Reflection • The reflected pulse is inverted. • That is, if an upward displaced pulse is incident towards a fixed end boundary, it will reflect and return as a downward displaced pulse. • Similarly, if a downward displaced pulse is incident towards a fixed end boundary, it will reflect and return as an upward displaced pulse.

9. Fixed End Reflection • The speed of the reflected pulse is the same as the speed of the incident pulse. • The wavelength of the reflected pulse is the same as the wavelength of the incident pulse. • The amplitude of the reflected pulse is less than the amplitude of the incident pulse.

10. Fixed End Reflection • Of course, it is not surprising that the speed of the incident and reflected pulse are identical since the two pulses are traveling in the same medium. • Since the speed of a wave (or pulse) is dependent upon the medium through which it travels, two pulses in the same medium will have the same speed.

11. Fixed End Reflection • A similar line of reasoning explains why the incident and reflected pulses have the same wavelength. • Every particle within the rope will have the same frequency. • Being connected to one another, they must vibrate at the same frequency. • Since the wavelength of a wave depends upon the frequency and the speed, two waves having the same frequency and the same speed must also have the same wavelength.

12. Fixed End Reflection • Finally, the amplitude of the reflected pulse is less than the amplitude of the incident pulse since some of the energy of the pulse was transmitted into the pole at the boundary. • The reflected pulse is carrying less energy away from the boundary compared to the energy that the incident pulse carried towards the boundary. • Since the amplitude of a pulse is indicative of the energy carried by the pulse, the reflected pulse has a smaller amplitude than the incident pulse.

13. Free End Reflection • Now consider what would happen if the end of the rope were free to move. Instead of being securely attached, suppose it is attached to a ring that is loosely fit around the pole. • Because the right end of the rope is no longer secured, the last particle of the rope will be able to move when a disturbance reaches it. • This end of the rope is referred to as a free end.

14. Free End Reflection • When the incident pulse reaches the end of the medium, the last particle of the rope can no longer interact with the first particle of the pole. • Since the rope and pole are no longer attached and interconnected, they will slide past each other. • The result is that the reflected pulse is not inverted. • Inversion is not observed in free end reflection.

15. http://www.youtube.com/watch?feature=player_embedded&v=11_fRmvzqIYhttp://www.youtube.com/watch?feature=player_embedded&v=11_fRmvzqIY

16. Transmission of a Pulse Across a Boundary from Less to More Dense • Let's consider a thin rope attached to a thick rope, with each rope held at opposite ends by people. And suppose that a pulse is introduced by the person holding the end of the thin rope. • less dense medium (the thin rope) towards more dense medium (the thick rope). • Upon reaching the boundary, the usual two behaviors will occur.

17. Transmission of a Pulse Across a Boundary from Less to More Dense • Upon reaching the boundary, the usual two behaviors will occur. • A portion of the energy carried by the incident pulse is reflected and returns towards the left end of the thin rope. • The disturbance that returns to the left after bouncing off the boundary is known as the reflected pulse. • A portion of the energy carried by the incident pulse is transmitted into the thick rope. The disturbance that continues moving to the right is known as the transmitted pulse.

18. Transmission of a Pulse Across a Boundary from Less to More Dense • Upon reaching the boundary, the usual two behaviors will occur. • A portion of the energy carried by the incident pulse is transmitted into the thick rope. • The disturbance that continues moving to the right is known as the transmitted pulse.

19. Transmission of a Pulse Across a Boundary from Less to More Dense

20. Transmission of a Pulse Across a Boundary from Less to More Dense • Comparisons can also be made between the characteristics of the transmitted pulse and those of the reflected pulse. • The transmitted pulse (in the more dense medium) is traveling slower than the reflected pulse (in the less dense medium). • The transmitted pulse (in the more dense medium) has a smaller wavelength than the reflected pulse (in the less dense medium). • The speed and the wavelength of the reflected pulse are the same as the speed and the wavelength of the incident pulse.

21. Transmission of a Pulse Across a Boundary from Less to More Dense • In this case, the transmitted and reflected pulses are traveling in two distinctly different media. • Waves always travel fastest in the least dense medium. • Thus, the reflected pulse will be traveling faster than the transmitted pulse.

22. Transmission of a Pulse Across a Boundary from Less to More Dense • Second, particles in the more dense medium will be vibrating with the same frequency as particles in the less dense medium. • Since the transmitted pulse was introduced into the more dense medium by the vibrations of particles in the less dense medium, they must be vibrating at the same frequency. • So the reflected and transmitted pulses have the different speeds but the same frequency. • Since the wavelength of a wave depends upon the frequency and the speed, the wave with the greatest speed must also have the greatest wavelength.

23. Transmission of a Pulse Across a Boundary from Less to More Dense • Finally, the incident and the reflected pulse share the same medium. • Since the two pulses are in the same medium, they will have the same speed. • Since the reflected pulse was created by the vibrations of the incident pulse, they will have the same frequency. • And two waves with the same speed and the same frequency must also have the same wavelength.

24. http://www.physicsclassroom.com/mmedia/waves/ltm.cfm

25. Transmission of a Pulse Across a Boundary from More to Less Dense • Finally, let's consider a thick rope attached to a thin rope, with the incident pulse originating in the thick rope. • more dense medium (thick rope) towards less dense medium (thin rope). • There will be partial reflection and partial transmission at the boundary. The reflected pulse in this situation will not be inverted. Similarly, the transmitted pulse is not inverted (as is always the case). Since the incident pulse is in a heavier medium, when it reaches the boundary, the first particle of the less dense medium does not have sufficient mass to overpower the last particle of the more dense medium. The result is that an upward displaced pulse incident towards the boundary will reflect as an upward displaced pulse. For the same reasons, a downward displaced pulse incident towards the boundary will reflect as a downward displaced pulse.

26. Transmission of a Pulse Across a Boundary from More to Less Dense • The reflected pulse in this situation will not be inverted. • Similarly, the transmitted pulse is not inverted (as is always the case). • Since the incident pulse is in a heavier medium, when it reaches the boundary, the first particle of the less dense medium does not have sufficient mass to overpower the last particle of the more dense medium. • The result is that an upward displaced pulse incident towards the boundary will reflect as an upward displaced pulse.

27. Transmission of a Pulse Across a Boundary from More to Less Dense • Comparisons between the characteristics of the transmitted pulse and the reflected pulse lead to the following observations. • The transmitted pulse (in the less dense medium) is traveling faster than the reflected pulse (in the more dense medium). • The transmitted pulse (in the less dense medium) has a larger wavelength than the reflected pulse (in the more dense medium). • The speed and the wavelength of the reflected pulse are the same as the speed and the wavelength of the incident pulse.

28. Transmission of a Pulse Across a Boundary from More to Less Dense

30. Boundary Behavior • The boundary behavior of waves in ropes can be summarized by the following principles: • The wave speed is always greatest in the least dense rope. • The wavelength is always greatest in the least dense rope. • The frequency of a wave is not altered by crossing a boundary. • The reflected pulse becomes inverted when a wave in a less dense rope is heading towards a boundary with a more dense rope. • The amplitude of the incident pulse is always greater than the amplitude of the reflected pulse.

31. Behavior of Waves • 4.1 Boundary Behavior • 4.2 Reflection, Refraction, Diffraction • 4.3 Interference of Waves • 4.4 The Doppler Effect

32. Reflection, Refraction, Diffraction • The wave doesn't just stop when it reaches the end of the medium. • Rather, a wave will undergo certain behaviors when it encounters the end of the medium. • Specifically, there will be some reflection off the boundary and some transmission into the new medium.

33. Reflection, Refraction, Diffraction • But what if the wave is traveling in a two-dimensional medium such as a water wave traveling through ocean water? • Or what if the wave is traveling in a three-dimensional medium such as a sound wave or a light wave traveling through air? • What types of behaviors can be expected of such two- and three-dimensional waves?

34. Reflection, Refraction, Diffraction • Use ripple tanks to show the behavior of waves

35. Reflection, Refraction, Diffraction

36. Reflection, Refraction, Diffraction • Create a source of straight waves. • These straight waves have alternating crests and troughs. • As viewed on the sheet of paper below the tank, the crests are the dark lines stretching across the paper and the troughs are the bright lines.

37. Reflection, Refraction, Diffraction • These waves will travel through the water until they encounter an obstacle - such as the wall of the tank or an object placed within the water • The direction that these wavefronts (straight-line crests) are traveling through the water is represented by the blue arrow. • The blue arrow is called a ray and is drawn perpendicular to the wavefronts..

38. Reflection, Refraction, Diffraction • Upon reaching the barrier placed within the water, these waves bounce off the water and head in a different direction.

39. Reflection, Refraction, Diffraction • Regardless of the angle at which the wavefronts approach the barrier, one general law of reflection holds true: • the waves will always reflect in such a way that the angle at which they approach the barrier equals the angle at which they reflect off the barrier. • This is known as the law of reflection.

40. Reflection, Refraction, Diffraction

41. Reflection, Refraction, Diffraction • The discussion above pertains to the reflection of waves off of straight surfaces. • But what if the surface is curved, perhaps in the shape of a parabola? • Several wavefronts are approaching the barrier; the ray is drawn for these wavefronts.

42. Reflection, Refraction, Diffraction • Upon reflection off the parabolic barrier, the water waves will change direction and head towards a point. • It is as though all the energy being carried by the water waves is converged at a single point - the point is known as the focal point. • After passing through the focal point, the waves spread out through the water.

43. Refraction • Reflection involves a change in direction of waves when they bounce off a barrier. • Refractionof waves involves a change in the direction of waves as they pass from one medium to another. • Refraction, or the bending of the path of the waves, is accompanied by a change in speed and wavelength of the waves.

44. Refraction • If the medium (and its properties) is changed, the speed of the waves is changed. • The most significant property of water that would affect the speed of waves traveling on its surface is the depth of the water. Water waves travel fastest when the medium is the deepest. Thus, if water waves are passing from deep water into shallow water, they will slow down.

45. Refraction • This decrease in speed will also be accompanied by a decrease in wavelength. • So as water waves are transmitted from deep water into shallow water, the speed decreases, the wavelength decreases, and the direction changes.

46. Refraction • Waves traveling from the deep end to the shallow end can be seen to refract (i.e., bend), decrease wavelength (the wavefronts get closer together), and slow down (they take a longer time to travel the same distance).

47. Refraction • When traveling from deep water to shallow water, the waves are seen to bend in such a manner that they seem to be traveling more perpendicular to the surface. • If traveling from shallow water to deep water, the waves bend in the opposite direction.

48. Diffraction • Reflection involves a change in direction of waves when they bounce off a barrier; • refraction of waves involves a change in the direction of waves as they pass from one medium to another; • and diffraction involves a change in direction of waves as they pass through an opening or around a barrier in their path.

49. Diffraction • Diffraction can be demonstrated by placing small barriers and obstacles in a ripple tank and observing the path of the water waves as they encounter the obstacles. • The waves are seen to pass around the barrier into the regions behind it; subsequently the water behind the barrier is disturbed.

50. Diffraction