1. The Nature of Waves Physics Montwood High School R. Casao

2. Energy Transfer – –A wave is a disturbance that propagates through a medium or space. A wave cannot exist in one place but must extend from one place to another. – –Waves provide a mechanism by which energy is transmitted from one location to another without the physical transfer of matter between these locations. – –The source of all waves is something that is vibrating.

3. TYPES OF WAVES Waves TYPES OF WAVES Waves are classified into different types according to their natures :

4. Mechanical Waves Mechanical waves: those that require a medium to pass through. Medium: any region through which a wave disturbance propagates. To generate mechanical waves, a source of energy is required to cause a disturbance and an elastic medium is required to transmit the disturbance. Sound waves and ocean waves are examples of mechanical waves. Without the medium - air, water, etc. - there can be no wave propagation.

5. Mechanical Waves An elastic medium behaves as if it were an array of particles connected to springs with each particle occupying an equilibrium position. A displacement produced by an energy source travels from particle to particle.

6. Longitudinal Waves Longitudinal wave: a wave in which the displacement of particles of the medium is parallel to the direction of propagation of the wave. Compression: the region of the longitudinal wave in which the distances separating the vibrating particles is less than their equilibrium position. – –When a compression is released, it attempts to return to its equilibrium position. Thus they compress the region adjacent to the compressions. Rarefaction: the region of a longitudinal wave in which the vibrating particles are farther apart than their equilibrium position. – –Rarefactions travel along a medium just as compressions do.

7. Longitudinal Waves Longitudinal wave motion: continuous wave disturbance parallel to the direction the pulses are traveling. Energy is transferred from particle to particle along the medium without motion of the medium as a whole.

8. Sound Waves Molecules in the air vibrate about some average position creating the compressions and rarefactions. We call the frequency of sound the pitch.

9. Longitudinal Waves Longitudinal and Transverse Wave Motion Illustrations Longitudinal and Transverse Wave Motion Waves

10. Transverse Waves Transverse wave: a wave in which the displacement of particles of the medium is perpendicular to the direction of propagation of the wave. Pulse: a single non-repeated disturbance. Crest: upward displacement (positive pulse). Trough: downward displacement (negative pulse). The displacement of the particles of the medium caused by the pulse are perpendicular to the direction in which the pulse travels. – –If a pulse is produced in the middle of a medium, the disturbance will move in both directions.

11. Transverse Waves Longitudinal and Transverse Wave Motion Illustrations Longitudinal and Transverse Wave Motion Waves

12. Electromagnetic Waves Electromagnetic waves: can travel through a vacuum; they do not require a material medium for their propagation. Disturbance of electric and magnetic fields travelling through space. All electromagnetic waves are transverse waves. Light, radio waves, television waves, microwaves, and x-rays are examples of electromagnetic waves. Speed: 3 x 10 8 m/s

13. Characteristics of Waves Frequency (f ): the number of crests (or troughs) passing a given point in a unit time, usually a second; number of vibrating oscillations, or cycles, per unit time. – –Unit: hertz, Hz. – –One hertz is equivalent to one cycle per second; dimensionally it is s -1.

14. Characteristics of Waves Period (T): amount of time required for one complete oscillation. Period is the reciprocal of frequency; Period is measured in seconds.

15. Characteristics of Waves Wavelength ( ): is the distance between two points that occupy the same relative position on the wave. Wavelength is the distance advanced by the wave motion in one period and is often measured from crest to crest along a wave or from trough to trough along a wave.

17. Characteristics of Waves Amplitude: maximum displacement of vibrating particles of the medium from their equilibrium positions.

18. Characteristics of Waves The amplitude of a wave is related to the energy which it transports.

19. Characteristics of Waves

20. Wave Speed Waves move with a speed that is related to frequency and wavelength. In general, waves travel with a speed: Speed of light (electromagnetic radiation): 3 x 10 8 m/s Speed of sound in air: 334 m/s (although it varies with air temperature)

21. Wave Interactions Reflection: – –A wave is turned back, or reflected, when it encounters a barrier that is the boundary of the medium in which the wave is traveling. – –Angle of incidence (i): the angle between the incident wave and the normal (perpendicular) drawn to the point of incidence. – –Angle of reflection (r): the angle between the reflected wave and the normal drawn to the point of incidence. – –The angle of incidence equal to the angle of reflection; i = r.

22. Wave Interactions Law of Reflection: when a wave disturbance is reflected at the boundary of a transmitting medium, the angle of incidence is equal to the angle of reflection.

24. Refraction refers to the change in direction of a wave at a boundary where the wave passes from one transparent medium into another. When a wave is incident on a boundary between media, some of the wave’s energy is reflected and some is transmitted. For example, when light traveling in air is incident on a transparent material such as glass, it is partially reflected and partially transmitted. – –The direction of the transmitted light is different from the direction of the incident light, so the light is said to have been refracted; in other words, it has changed direction.

26. The change in direction is caused by the fact that light travels with different speeds in different media. The passage of light takes longer thru a medium with more atoms per volume; the speed of light is less in denser media. The change in the direction of wave propagation is described by the angle of refraction. Angle of incidence =  1 ; angle of refraction =  2 Snell’s law describes the relationship between the angles of incidence and refraction and the speed of light in two media:

28. Note that  1 and  2 are measured with respect to the normal. Light is refracted when passing from one medium into another because the speed of light is different in the two media. The speed of light is greatest in a vacuum, and it is convenient to compare the speed of light in other media with the speed of light c; this is done by defining a ratio called the index of refraction n:

29. Altho the table containing indices of refraction lists n air = 1.00029, you can assume n air = 1. A more practical form of Snell’s law is: The following relationships are described by Snell’s law: 1. 1.If the second medium is more optically dense than the first medium (n 2 > n 1 ), the ray is refracted toward the normal (  2 <  1 ); see figure a next slide. 2. 2.If the second medium is less optically dense than the first medium (n 2  1 ); see figure b next slide.

30. Index of refraction and ray deviation

31. The change in direction and the change in speed occur simultaneously. Remember as light travels from one medium to another its wavelength changes, NOT its frequency.

33. Wave Interactions Diffraction refers to the bending of waves around an edge of an object and is not related to refraction. – –Example: if you stand along the outside wall of a building near the corner, you can hear people talking around the corner. –Assuming no reflections or air motion, this would not be possible if the sound waves traveled in a straight line.

34. – –As the sound waves pass the corner, instead of being in a dead zone, they wrap around the edge and you can hear the sound. When a traveling water wave hits an obstacle, the wave fronts spreads out round the edge and becomes curved. The wavelength of the wave is not changed in diffraction.

35. Doppler Effect The Doppler shift (sometimes called the Doppler effect) is a change in frequency of emitted waves produced by motion of an emitting source relative to an observer. The Doppler shift (sometimes called the Doppler effect) is a change in frequency of emitted waves produced by motion of an emitting source relative to an observer. You hear the high pitch of the siren of an approaching ambulance and notice that the pitch drops suddenly as the ambulance passes you. This is an example of the Doppler effect. You hear the high pitch of the siren of an approaching ambulance and notice that the pitch drops suddenly as the ambulance passes you. This is an example of the Doppler effect. Movement alters the wavelength and the received frequency of sound, even though the source frequency and sound velocity are unchanged. Movement alters the wavelength and the received frequency of sound, even though the source frequency and sound velocity are unchanged. Applet:http://www.colorado.edu/physics/2000/applet s/doppler.html Applet:http://www.colorado.edu/physics/2000/applet s/doppler.html http://paws.kettering.edu/~drussell/Demos/doppler/ doppler.html http://paws.kettering.edu/~drussell/Demos/doppler/ doppler.html

36. Resting Sound Source source at rest observer at rest Frequency f s Frequency f o V=340m/s

37. Sound Source Moving Toward Observer sourceobserver at rest Frequency f s Frequency f o Observer hears increased pitch (shorter wave length)

38. Sound Source Moving Towards Observer f o = frequency heard by observer f s = frequency of source v = velocity of wave in the medium v s = velocity of source

39. Source Moving In the above equation – v s is used when the source moves towards the observer. This makes sense because the observed frequency is expected to increase as the source moves towards the observer. When the source moves away from the observer, + v s is used.

40. Sound Source Moving Away from Observer source observer at rest Frequency f s Frequency f o Observer hears decreased pitch (longer wave length)

41. Moving Observer v o = velocity of observer

42. Moving Observer In the above equation + v o is used when the observer moves towards the source and – v o is used when the observer moves away from the source.

43. Doppler Effect General Case +v o is used when the observer moves towards the source, –v o is used when the observer moves away from the source, –v s is used when the source moves towards the observer, and +v s is used when the source moves away from the observer.

45. Application of Doppler Effect Nexrad: Nex t Generation Weather Rad ar

46. Doppler Flow Meter A Doppler flow meter measures the speed of red blood cells.

47. EM Radiation and the Doppler Effect c = speed of light v S = the relative velocity between the source and the listener: positive when source moves away from the listener; negative when the source moves toward the listener.

48. Wave Interference When two wave pass each other their superposition causes reinforcement or cancellation. Works for both longitudinal waves and for transverse waves. Overlapping waves algebraically add to produce a. Overlapping waves algebraically add to produce a resultant wave. Overlapping waves do not in any way alter the travel of each other.

49. Principle of Superposition Simply align the waves in time and add the amplitudes. Amplitudes can be either positive or negative. If the amplitudes are of the same sign, the wave is reinforced and grows bigger. If the amplitudes are of opposite sign, the wave is diminished and grows smaller.

50. Wave Interference

51. Interference of Waves

52. Constructive Interference Reinforcement when the crest of one wave overlaps the crest of another. Their individual effects adds together, resulting in a wave increased in amplitude.

53. Destructive Interference Cancellation when crest of one wave overlaps trough of another reducing their individual effects. Water waves show these best. – –Out of phase- the crest of one wave arrives at a point at the same time as a trough of the second wave arrives, effects cancel each other. – –In phase- two waves crests and troughs arrive at a place at the same time, effects reinforce each other.

54. Sound Wave Interference  Interference occurs when two sounds of difference frequency are heard superposed.  Constructive interference causes louder sound and destructive inference cause fainter sound.  This alternating pattern produces a beat. A piano tuner listens for beats to disappear.

55. Water Wave Interference Left side is a theoretical drawing of an interference pattern. Right side is the actual interference pattern.

56. Polarization of Light Waves The electric and magnetic field vectors associated with an EM wave are at right angles to each other and also to the direction of wave propagation. Polarization is evidence of the transverse nature of EM waves.

57. An beam of light consists of a large number of EM waves emitted by the atoms or molecules of the light source. The vibrating charges associated with the atoms act as tiny antennas with each atom producing a wave with its own orientation of the electric field corresponding to the direction of atomic vibration. Because all directions of vibration are possible, the resultant EM wave is a superposition of waves produced by the individual atomic sources. The result is an unpolarized light wave as shown.

58. The direction of wave propagation shown is perpendicular to the page. All directions of the electric field vector are equally probable and lie in a plane (such as the plane of the page) perpendicular to the direction of propagation.

59. A wave is linearly polarized if the resultant electric field vibrates in the same direction at all times at a particular point; also called plane polarized or just polarized. The wave to the right is polarized in the y- direction; as the wave propagates in the x- direction, the electric field is always in the y-direction. It’s possible to obtain a linearly polarized beam from an unpolarized beam by removing all waves from the beam except those with electric field vectors that oscillate in a single plane.

60. Most common technique for polarizing light is to use a material that transmits waves having electric field vectors that vibrate in a plane parallel to a certain direction and absorbs those waves with electric field vectors vibrating in directions perpendicular to that direction.

62. Problem Example A sound wave has a frequency of 262 Hz and a wavelength of 1.29 m. a. What is the speed of the wave? b. How long will it take the wave to travel the length of a football field, 91.4 m?

63. Problem Example c. c. What is the period of the wave?

64. Homework Conversions Megahertz and hertz: 1 MHz = 1 x 10 6 Hz Meters and nanometers: 1 m = 1 x 10 9 nm 1 x 10 -9 m = 1 nm