2. Waves AP Physics 1

3. Standards Essential Knowledge 3.B.3: Restoring forces can result in oscillatory motion. When linear restoring force is entered on an object displacement from an equilibrium position, the object will undergo a special type of motion called simple harmonic motion (SMH). -Examples should include gravitational force exerted by earth on a simple pendulum and mass- spring oscillator. a. For a spring that exerts a linear restoring force, the period of a mass-spring oscillator increases with mass and decreases with spring stiffness. b. For a simple pendulum, the period increases with the length of the pendulum and decreases with the magnitude of the gravitational field. c. Minima, maxima, and zeros of position, velocity, and acceleration are features of harmonic motion. Students should be able to calculate force and acceleration for any given displacement for an object oscillating on a spring.

5. What is a wave? - A disturbance that propagates through space or a medium, and transports energy without transporting mass.

6. What is a Pulse? - A single vibratory disturbance that propagates through space or a medium, and transports energy and information but no mass.

7. Types of waves: Waves are classified into different types accordingly :

8. Mechanical Waves -A material is needed for the transmission. -C annot travel through vacuum.  Ex: Water waves, sound, vibration of spring

9. Electromagnetic Waves No medium is needed for propagation. They can travel through a vacuum. All electromagnetic waves are transverse.  Ex: X-rays, radio waves, micro-waves,etc

11. Transverse Waves 1. Appears as a sine curve. 2. The motions of the particles is Perpendicular to the direction of energy propagation – the direction the wave is moving 3. Ex: Pulse in a stretched string, light.

12. Longitudinal Waves 1. The motions of the particles is parallel to the direction that the energy propagates – the direction the wave travels. 2. Ex: Sound, or a spring oscillating back and forth.

13. Longitudinal waves  In sound the particles of the medium move back and fort creating regions of high and low density,or high or low pressure,  Condensations ( High Pressure) and Rarefactions (Low Pressure).

14. Types of waves: 1.Mechanical 2.Electromagnetic Mechanical Waves ocean waves seismic waves sound waves Electromagnetic Waves radio waves x-rays light

15. - Wave Speed - The speed depends on the “medium” it’s traveling in and the temperature. Type (temp) Speed  Sound in air at 20°C343 m/s = 767 miles/hour  Sound in air at 0°C331 m/s  Sound in water at 25°C 1493 m/s  Sound in aluminum5100 m/s  Light in vacuum 3 x 10 8 m/s = 186,000 miles/sec  Light in diamond1.2 x 10 8 m/s

16. Wave Properties - Wave Properties - A wave is described in terms of the following characteristics:  Amplitude  Wavelength ( )  Frequency (f )  Period (T)  Wave velocity (v)  Crest  Trough  Compression  Rarefaction  Nodes

17. Period and Frequency  P eriod ( T ) - Is the time it takes to complete one oscillation or vibration (measured in seconds) (sec/cycle)  Frequency - ( f ) the number of vibrations, oscillations or waves per unit time. (measured in 1/s or hertz) (cycles/sec)

18. are inverse of one another. Period and Frequency are inverse of one another.

19.  Amplitude - Maximum displacement from its equilibrium position.  Wavelength ( )- The minimum distance between two points which are in phase.

20. AmplitudeFrequency Sound Waves LoudnessPitch Light Waves Brightness ROYGBIV Red - Lowest frequency - Longest wavelength Violet -Highst frequency - Shortest wavelength

21. Wave Equation  The wave velocity is the displacement traveled by the wave in one second ……....  The velocity of the wave (v) is related to frequency (f) and wavelength ( ) by -

22. A wave travels one wavelength in one period. Thus, the speed (v): Wave Equation Derivation Since

23. A traveling wave of wavelength 1.0 m moves at a speed of 3.0 m/s. 1.What is the period of this wave? 2.What is the frequency of this wave? By using the wave equation, v = ƒ 3.0 m/s = ƒ(1.0 s) ƒ = 3.0 Hz Period T = 1/ƒ T = 1/3 Hz T=.333 sec

24. The diagram shows a piston being moved back and forth to generate a wave. The piston produces a compression, C, every 0.50 second. The frequency of this wave is 1.1.0 Hz 2.2.0 Hz 3.5.0 x 10 -1 Hz 4.3.3 x 10 2 Hz What is the angle between the direction of propagation of a transverse wave and the direction in which the amplitude of the wave is measured? 1.0 degrees 2.45 degrees 3.90 degrees 4.180 degrees

25. What is the period of a periodic wave that has the frequency of 60 hertz? a.1.7 x 10 -2 s b.2.0 x 10 4 s c.3.0 x 10 -3 s d.3.3 x 10 2 s A periodic wave with a frequency of 10 hertz would have a period of: a.1s b.0.1s c.10s d.100s

26. The echo is heard 2 seconds after a sonar wave reflects off the ocean floor which is 1170 meters away a.What is the waves speed ? b.If the frequency of the wave is 60Hz, what is it’s wavelength? c.What is the period of the wave?

27. A skipper on a boat notices wave crests passing his anchor chain every 5 seconds. If the wave crests are 15 m apart, what is the speed of the water waves in m/s? a.5 b.15 c.75 d.10 e.3

28. An elephant produces a 10 Hz sound wave. Assuming the speed of sound in air is 345 m/s, determine the wavelength of this infrasonic sound wave.

29. 1.Miles Tugo is camping in Glacier National Park. In the midst of a glacier canyon, he makes a loud holler. He hears an echo 2.0 s later. The air temperature is 20 0 C. How far away are the canyon walls. 2.Two sound waves are traveling through a container of nitrogen gas. Wave A has a wavelength of 1.5 m. Wave B has a wavelength of 4.5 m. The velocity of wave B must be _______ the velocity of wave A. a.one-ninth b.one-third c.the same as d.three times larger than

30. Speed of a Wave on a String  The speed on a wave stretched under some tension, F   is called the linear density  The speed depends only upon the properties of the medium through which the disturbance travels Section 13.9

31. Constructive Interference  Two waves, a and b, have the same frequency and amplitude  Are in phase  The combined wave, c, has the same frequency and a greater amplitude Section 13.10

32. Constructive Interference in a String  Two pulses are traveling in opposite directions  The net displacement when they overlap is the sum of the displacements of the pulses *Note that the pulses are unchanged after the interference

33. Destructive Interference  Two waves, a and b, have the same amplitude and frequency  One wave is inverted relative to the other  They are 180° out of phase  When they combine, the waveforms cancel

34.  Two pulses are traveling in opposite directions  The net displacement when they overlap is decreased since the displacements of the pulses subtract *Note that the pulses are unchanged after the interference Destructive Interference in a String

35. Reflection of Waves – Fixed End  Whenever a traveling wave reaches a boundary, some or all of the wave is reflected  When it is reflected from a fixed end, the wave is inverted  The shape remains the same

36. Reflected Wave – Free End  When a traveling wave reaches a boundary, all or part of it is reflected  When reflected from a free end, the pulse is not inverted

37. Polarization: the limiting of a vibrations of a wave to a single plane. Only transverse wave may be polarized. Waves may be polarized by Generation Filtering Reflection

38. Polarization of Light  Electromagnetic waves are transverse waves  Transverse waves are polarizable  Longitudinal waves, like sound waves, cannot be polarized

39. Polarizing filters: 1.Enhance blue skies and increase color saturation by reducing reflections 2.Reduce glare on streams and wet leaves. Non Polarized The unpolarized image looks flat, without saturated colors. Polarized Notice the more saturated colors, the blue in the sky and the colors in the trees. There is also a greater sense of depth and perspective.

40. The Doppler effect is the way a wave seems to increase or decrease in frequency when there is relative motion between the observer and the source of the wave. Have you ever stopped at a railroad crossing to let a train pass by? Did you notice that the sound of the train's whistle is higher pitched when the train was approaching and lower when it was receeding? Then you have witnessed the Doppler effect. Doppler Acapella Doppler Acapella (Link)

41. When a source of waves and an observer are moving towards each other: 1. A higher frequency is heard 2. A shorter wavelength is observed. When a source of waves and an observer are moving apart: 1.A lower frequency is heard 2.A longer wavelength is observed.

42. Weather radars send out radio waves. Objects in the air, such as rain drops, snow crystals, hail stones or even insects and dust, scatter or reflect some of the radio waves back to the antenna. Weather radars electronically convert the reflected radio waves into pictures showing the location and intensity of precipitation. Doppler radars also measure the frequency change in returning radio waves. Waves reflected by something moving away from the antenna change to a lower frequency. Waves from an object moving toward the antenna change to a higher frequency.

43. A particularly interesting example is used by astronomers to determine if Light emitting objects (such as stars) are getting closer to us or farther away. 1. If light (star) is moving away – lower frequency, long wavelength– red shifted 2. If light (star) is moving towards – higher frequency, short wavelength – blue shifted.

44. Red Shift

45. Case I : Stationary wave source

46. Case II : Wave velocity greater than the source velocity.

47. Case III : Wave velocity the same as the source velocity

48. Case IV : Wave velovity less than the source velocity(sound-sonic boom!).

49. When you move away from a fixed source of sound the frequency of the sound you hear: a.is greater than what the source emits b.is less than what the source emits c.is the same as what the source emits

50. A train whistle at rest has a frequency of 3000 Hertz. You are standing still and observe the frequency to be 3010 Hz, you can conclude that... a. the train is moving away from you b. the train is moving toward you c. the sound from the whistle has echoed d. not enough information is given

51. Doppler Effect, General Case  Both the source and the observer could be moving  Use positive values of v o and v s if the motion is toward  Frequency appears higher  Use negative values of v o and v s if the motion is away  Frequency appears lower Section 14.6

52. Doppler Effect, Source Moving – Equation  Use the –v s when the source is moving toward the observer and +v s when the source is moving away from the observer Section 14.6

53. Doppler Effect, Source Moving – Equation  Use the –v s when the source is moving toward the observer and +v s when the source is moving away from the observer Section 14.6

54. Occurs when energy is transferred to a system... at its natural frequency. Resonance

55. Natural Frequency...  Object composed of elastic material will vibrate at a natural frequency when disturbed  The natural frequency of a body depends on its... Elasticity Size shape Resonance

56.  Resonance occurs in all types of objects  When the applied frequency…..matches the natural frequency of the body.  The resulting vibration has a high amplitude possibly destroying the body.

57.  mass on a spring at resonance  swinging your legs in a swing  breaking a wine glass using sound  a tuning fork exciting a guitar string  a truck driving on a rough road  In 1940, the Tacoma Narrows Bridge was destroyed by wind- generated resonance.

58. Resonance in a ruler Hold a 30 cm rule loosely at one end between your thumb and first finger. Tap it and let it swing from side to side, so the frequency is about 1 Hz. Now try to keep the ruler swinging at the frequency. You should be able to do this with very slight hand movements. Notice how easy it is to get the ruler to make swings with a large amplitude. Without putting more effort into it, try to doubled the frequency of your hand movement. What has happened to the amplitude of the ruler's swing? Probably much smaller. If you’ve still got the same amplitude you may be putting in more effort than before. You will also get a smaller amplitude from the ruler if you decrease the frequency of your hand movement to well below 1 Hz.

59. Resonance in your bathroom. The air in your bathroom will have a resonant frequency. This means that if you hum notes of different pitches, one of them will sound louder than all the others. At this frequency the air is resonating, it’s oscillating with a bigger amplitude. So when you talk in there, your voice may sound a bit different - usually a bit boomy. Whilst this is fine in a bathroom, we don't want this effect in a loudspeaker.

60. If you push a person on a swing, you must put the energy in at just the natural frequency of the swing. In this animation, the energy is put in at the natural frequency of the pendulum. Notice how the energy builds constructively until it does work on the monkey's face. If you put the energy in too slow, you miss the swing being there to accept the energy. If you put it in too fast, you miss the swing more often. In this case the energy is put in at higher than the natural frequency of the pendulum. As a result of the destructive energy, the energy level does not build up.

61. If there is a second tuning fork nearby with the same Natural Frequency it will begin to vibrate also even though it hasn’t been struck.

62. Tacoma Narrows Bridge link

63. Resonance allows energy to be transferred to a vibrating object efficiently if the energy is delivered at the natural frequency of vibration. Tacoma Narrows Bridge Tacoma Narrows Bridge

64. How Earthquakes Make Buildings Vibrate Resonance in Buildings If the ground moved to and fro with a frequency of 5.5 Hz Tall building would vibrate strongly, or resonate Short building hardly moved. If the ground shook with a frequency of 7.5 Hertz, the small building would resonate while the tall building hardly moved at all.

65. Taller buildings tend to have a lower natural frequency than shorter buildings because they are more flexible. Buildings tend to have lower natural frequencies when they are heavier or more flexible.

66. Beat Frequency Beats are used to tune up musical instruments! BEATS : When two waves of slightly different frequencies interfere with each other.

67. The beat frequency is equal to the difference in the frequency of the two sounds. 1. What is the beat frequency when a 262 Hz and a 266 Hz tuning fork are sounded together? 2. What is the period of the beat in the previous problem?

68. One speaker is transmitting a 10 Hz signal and a second is transmitting a 11 Hz signal. What beat frequency is experienced?

69. The waves interfere with each other alternatively constructive and destructive.