1. Section 1 Simple Harmonic Motion
Chapter 12
Objectives
Identify the conditions of simple harmonic motion.
Explain how force, velocity, and acceleration change as an object vibrates with simple harmonic motion.
Calculate the spring force using Hooke’s law.

2. Simple Harmonic Motion
Section 1 Simple Harmonic Motion
Simple Harmonic Motion
Motion that repeats in a regular pattern over and over again is called periodic motion.

3. Section 1 Simple Harmonic Motion
Hooke’s Law
One type of periodic motion is the motion of a mass attached to a spring.
The direction of the force acting on the mass (Felastic) is always opposite the direction of the mass’s displacement from equilibrium (x = 0).

4. Hooke’s Law, continued At equilibrium:
Section 1 Simple Harmonic Motion
Hooke’s Law, continued
At equilibrium:
The spring force and the mass’s acceleration become zero.
The speed reaches a maximum.
At maximum displacement:
The spring force and the mass’s acceleration reach a maximum.
The speed becomes zero.

5. spring force = –(spring constant  displacement)
Section 1 Simple Harmonic Motion
Hooke’s Law, continued
Measurements show that the spring force, Felastic or restoring force, is directly proportional to the displacement of the mass.
This relationship is known as Hooke’s Law:
Felastic = –kx
spring force = –(spring constant  displacement)
The quantity k is a positive constant called the spring constant.

7. Chapter 11 Sample Problem Hooke’s Law
Section 1 Simple Harmonic Motion
Chapter 11
Sample Problem
Hooke’s Law
If a mass of 0.55 kg attached to a vertical spring stretches the spring 2.0 cm from its original equilibrium position, what is the spring constant?

8. Sample Problem, continued
Section 1 Simple Harmonic Motion
Chapter 11
Sample Problem, continued
3. Calculate
Substitute the values into the equation and solve:
4. Evaluate
The value of k implies that 270 N of force is required to displace the spring 1 m.

10. https://sites.google.com/site/physicsflash/home/shm
Section 1 Simple Harmonic Motion
Chapter 11
Spring Constant

11. Hooke’s Law The spring constant can be determined experimentally
Measure the displacement (x) and the corresponding restoring force (F)
Gather several data points
Plot Force vs Displacement
Draw a trend line
Calculate the slope

12. Hooke’s Law
The slope of the line on a Force vs Displacement graph is the spring constant (k)
It must be a positive number, greater than zero
If the data shows something else, there is a problem

14. Simple Harmonic Motion
Section 1 Simple Harmonic Motion
Chapter
Simple Harmonic Motion
Simple harmonic motion describes any periodic motion that is the result of a restoring force that is proportional to displacement.
Because simple harmonic motion involves a restoring force, every simple harmonic motion is a back-and-forth motion over the same path.

15. Simple Harmonic Motion
Section 1 Simple Harmonic Motion
Chapter
Simple Harmonic Motion

17. Chapter The Simple Pendulum
Section 1 Simple Harmonic Motion
Chapter
The Simple Pendulum
A simple pendulum consists of a mass called a bob, which is attached to a fixed string.
The forces acting on the bob at any point are the force exerted by the
string and the
gravitational force.

19. Chapter Objectives Identify the amplitude of vibration.
Section 2 Measuring Simple Harmonic Motion
Chapter
Objectives
Identify the amplitude of vibration.
Recognize the relationship between period and frequency.
Calculate the period and frequency of an object vibrating with simple harmonic motion.

20. Amplitude, Period, and Frequency in SHM
Section 2 Measuring Simple Harmonic Motion
Chapter
Amplitude, Period, and Frequency in SHM
In SHM, the maximum displacement from equilibrium is defined as the amplitude of the vibration.
A pendulum’s amplitude can be measured by the angle between the pendulum’s equilibrium position and its maximum displacement.
For a mass-spring system, the amplitude is the maximum amount the spring is stretched or compressed from its equilibrium position.
The SI units of amplitude are the meter (m).

21. Amplitude, Period, and Frequency in SHM
Section 2 Measuring Simple Harmonic Motion
Chapter
Amplitude, Period, and Frequency in SHM
The period (T) is the time that it takes a complete cycle to occur.
The SI unit of period is seconds (s).
The frequency (f) is the number of cycles or vibrations per second (1/s, s-1)
The SI unit of frequency is hertz (Hz).
Hz = s–1

22. Amplitude, Period, and Frequency in SHM, continued
Section 2 Measuring Simple Harmonic Motion
Chapter
Amplitude, Period, and Frequency in SHM, continued
Period and frequency are inversely related:
Thus, any time you have a value for period or frequency, you can calculate the other value.

23. Measures of Simple Harmonic Motion
Section 2 Measuring Simple Harmonic Motion
Chapter
Measures of Simple Harmonic Motion

24. click here for video Chapter Big Ben’s pendulum
Section 2 Measuring Simple Harmonic Motion
Chapter
Big Ben’s pendulum
click here for video

25. Period of a Simple Pendulum in SHM
Section 2 Measuring Simple Harmonic Motion
Chapter
Period of a Simple Pendulum in SHM
The period of a simple pendulum depends on the length and on the free-fall acceleration.
The period does not depend on the mass of the bob or on the amplitude.

26. Period of a Simple Pendulum in SHM
Section 2 Measuring Simple Harmonic Motion
Chapter
Period of a Simple Pendulum in SHM
The length of a pendulum is measured from the pivot point to the center of gravity of the bob

28. Section 3 Properties of Waves
Chapter 11
Objectives
Distinguish local particle vibrations from overall wave motion.
Differentiate between pulse waves and periodic waves.
Interpret waveforms of transverse and longitudinal waves.
Apply the relationship among wave speed, frequency, and wavelength to solve problems.
Relate energy and amplitude.

29. Chapter 11 Wave Motion A wave is the motion of a disturbance.
Section 3 Properties of Waves
Chapter 11
Wave Motion
A wave is the motion of a disturbance.
A medium is a physical environment through which a disturbance can travel. For example, water is the medium for ripple waves in a pond.
Waves that require a medium through which to travel are called mechanical waves. Water waves and sound waves are mechanical waves.
Electromagnetic waves such as visible light do not require a medium.

30. Section 3 Properties of Waves
Chapter 11
Wave Types
A wave that consists of a single traveling pulse is called a pulse wave.
Whenever the source of a wave’s motion is a periodic motion, such as the motion of your hand moving up and down repeatedly, a periodic wave is produced.
A wave whose source vibrates with simple harmonic motion is called a sine wave. Thus, a sine wave is a special case of a periodic wave in which the periodic motion is simple harmonic.

31. Relationship Between SHM and Wave Motion
Section 3 Properties of Waves
Chapter 11
Relationship Between SHM and Wave Motion
As the sine wave created by this vibrating blade travels to the right, a single point on the string vibrates up and down with simple harmonic motion.

32. Chapter 11 Wave Types, continued Section 3 Properties of Waves
A transverse wave is a wave whose particles vibrate perpendicularly to the direction of the wave motion.
The crest is the highest point above the equilibrium position, and the trough is the lowest point below the equilibrium position.
The wavelength (l) is the distance between two adjacent similar points of a wave.

33. Section 3 Properties of Waves
Chapter 11
Transverse Waves

34. Chapter 11 Wave Types, continued Section 3 Properties of Waves
A longitudinal wave is a wave whose particles vibrate parallel to the direction the wave is traveling.
A longitudinal wave on a spring at some instant t can be represented by a graph. The crests correspond to compressed regions, and the troughs correspond to stretched regions.
The crests are regions of high density and pressure (relative to the equilibrium density or pressure of the medium), and the troughs are regions of low density and pressure.

35. Section 3 Properties of Waves
Chapter 11
Longitudinal Waves

36. Period, Frequency, and Wave Speed
Section 3 Properties of Waves
Chapter 11
Period, Frequency, and Wave Speed
The frequency of a wave describes the number of waves that pass a given point in a unit of time.
The period of a wave describes the time it takes for a complete wavelength to pass a given point.
The relationship between period and frequency in SHM holds true for waves as well; the period of a wave is inversely related to its frequency.

37. Characteristics of a Wave
Section 3 Properties of Waves
Chapter 11
Characteristics of a Wave

38. Period, Frequency, and Wave Speed, continued
Section 3 Properties of Waves
Chapter 11
Period, Frequency, and Wave Speed, continued
The speed of a mechanical wave is constant for any given medium.
The speed of a wave is given by the following equation:
v = fl
wave speed = frequency  wavelength
This equation applies to both mechanical and electromagnetic waves.

39. Waves and Energy Transfer
Section 3 Properties of Waves
Chapter 11
Waves and Energy Transfer
Waves transfer energy by the vibration of matter.
Waves are often able to transport energy efficiently.
The rate at which a wave transfers energy depends on the amplitude.
The greater the amplitude, the more energy a wave carries in a given time interval.
For a mechanical wave, the energy transferred is proportional to the square of the wave’s amplitude.
The amplitude of a wave gradually diminishes over time as its energy is dissipated.

40. Chapter 11 Objectives Apply the superposition principle.
Section 4 Wave Interactions
Chapter 11
Objectives
Apply the superposition principle.
Differentiate between constructive and destructive interference.
Predict when a reflected wave will be inverted.
Predict whether specific traveling waves will produce a standing wave.
Identify nodes and antinodes of a standing wave.

41. Chapter 11 Wave Interference
Section 4 Wave Interactions
Chapter 11
Wave Interference
Two different material objects can never occupy the same space at the same time.
Because mechanical waves are not matter but rather are displacements of matter, two waves can occupy the same space at the same time.
The combination of two overlapping waves is called superposition.

42. Wave Interference, continued
Section 4 Wave Interactions
Chapter 11
Wave Interference, continued
In constructive interference, individual displacements on the same side of the equilibrium position are added together to form the resultant wave.

43. Wave Interference, continued
Section 4 Wave Interactions
Chapter 11
Wave Interference, continued
In destructive interference, individual displacements on opposite sides of the equilibrium position are added together to form the resultant wave.

44. Section 4 Wave Interactions
Chapter 11
Reflection
What happens to the motion of a wave when it reaches a boundary?
At a free boundary, waves are reflected.
At a fixed boundary, waves are reflected and inverted.
Free boundary Fixed boundary

45. Chapter 11 Standing Waves
Section 4 Wave Interactions
Chapter 11
Standing Waves
A standing wave is a wave pattern that results when two waves of the same frequency, wavelength, and amplitude travel in opposite directions and interfere.
Standing waves have nodes and antinodes.
A node is a point in a standing wave that maintains zero displacement.
An antinode is a point in a standing wave, halfway between two nodes, at which the largest displacement occurs.

46. Standing Waves, continued
Section 4 Wave Interactions
Chapter 11
Standing Waves, continued
Only certain wavelengths produce standing wave patterns.
The ends of the string must be nodes because these points cannot vibrate.
A standing wave can be produced for any wavelength that allows both ends to be nodes.
In the diagram, possible wavelengths include 2L (b), L (c), and 2/3L (d).

47. Chapter 11 Standing Waves Section 4 Wave Interactions
This photograph shows four possible standing waves that can exist on a given string. The diagram shows the progression
of the second standing wave for one-half of a cycle.

48. Chapter 11 Multiple Choice
Standardized Test Prep
Multiple Choice
Base your answers to questions 1–6 on the information below.
A mass is attached to a spring and moves with simple harmonic motion on a frictionless horizontal surface.
1. In what direction does the restoring force act?
A. to the left
B. to the right
C. to the left or to the right depending on whether the spring is stretched or compressed
D. perpendicular to the motion of the mass

49. Chapter 11 Multiple Choice
Standardized Test Prep
Multiple Choice
Base your answers to questions 1–6 on the information below.
A mass is attached to a spring and moves with simple harmonic motion on a frictionless horizontal surface.
1. In what direction does the restoring force act?
A. to the left
B. to the right
C. to the left or to the right depending on whether the spring is stretched or compressed
D. perpendicular to the motion of the mass

50. Multiple Choice, continued
Chapter 11
Standardized Test Prep
Multiple Choice, continued
Base your answers to questions 1–6 on the information below.
A mass is attached to a spring and moves with simple harmonic motion on a frictionless horizontal surface.
2. If the mass is displaced –0.35 m from its equilibrium position, the restoring force is 7.0 N. What is the spring constant?
F. –5.0  10–2 N/m H. 5.0  10–2 N/m
G. –2.0  101 N/m J. 2.0  101 N/m

51. Multiple Choice, continued
Chapter 11
Standardized Test Prep
Multiple Choice, continued
Base your answers to questions 1–6 on the information below.
A mass is attached to a spring and moves with simple harmonic motion on a frictionless horizontal surface.
2. If the mass is displaced –0.35 m from its equilibrium position, the restoring force is 7.0 N. What is the spring constant?
F. –5.0  10–2 N/m H. 5.0  10–2 N/m
G. –2.0  101 N/m J. 2.0  101 N/m

52. Multiple Choice, continued
Chapter 11
Standardized Test Prep
Multiple Choice, continued
Base your answers to questions 1–6 on the information below.
A mass is attached to a spring and moves with simple harmonic motion on a frictionless horizontal surface.
3. In what form is the energy in the system when the mass passes through the equilibrium point?
A. elastic potential energy
B. gravitational potential energy
C. kinetic energy
D. a combination of two or more of the above

53. Multiple Choice, continued
Chapter 11
Standardized Test Prep
Multiple Choice, continued
Base your answers to questions 1–6 on the information below.
A mass is attached to a spring and moves with simple harmonic motion on a frictionless horizontal surface.
3. In what form is the energy in the system when the mass passes through the equilibrium point?
A. elastic potential energy
B. gravitational potential energy
C. kinetic energy
D. a combination of two or more of the above

54. Multiple Choice, continued
Chapter 11
Standardized Test Prep
Multiple Choice, continued
Base your answers to questions 1–6 on the information below.
A mass is attached to a spring and moves with simple harmonic motion on a frictionless horizontal surface.
4. In what form is the energy in the system when the mass is at maximum displacement?
F. elastic potential energy
G. gravitational potential energy
H. kinetic energy
J. a combination of two or more of the above

55. Multiple Choice, continued
Chapter 11
Standardized Test Prep
Multiple Choice, continued
Base your answers to questions 1–6 on the information below.
A mass is attached to a spring and moves with simple harmonic motion on a frictionless horizontal surface.
4. In what form is the energy in the system when the mass is at maximum displacement?
F. elastic potential energy
G. gravitational potential energy
H. kinetic energy
J. a combination of two or more of the above

56. Multiple Choice, continued
Chapter 11
Standardized Test Prep
Multiple Choice, continued
Base your answers to questions 1–6 on the information below.
A mass is attached to a spring and moves with simple harmonic motion on a frictionless horizontal surface.
5. Which of the following does not affect the period of the mass-spring system?
A. mass
B. spring constant
C. amplitude of vibration
D. All of the above affect the period.

57. Multiple Choice, continued
Chapter 11
Standardized Test Prep
Multiple Choice, continued
Base your answers to questions 1–6 on the information below.
A mass is attached to a spring and moves with simple harmonic motion on a frictionless horizontal surface.
5. Which of the following does not affect the period of the mass-spring system?
A. mass
B. spring constant
C. amplitude of vibration
D. All of the above affect the period.

58. Multiple Choice, continued
Chapter 11
Standardized Test Prep
Multiple Choice, continued
Base your answers to questions 1–6 on the information below.
A mass is attached to a spring and moves with simple harmonic motion on a frictionless horizontal surface.
6. If the mass is 48 kg and the spring constant is 12 N/m, what is the period of the oscillation?
F. 8p s H. p s
G. 4p s J. p/2 s

59. Multiple Choice, continued
Chapter 11
Standardized Test Prep
Multiple Choice, continued
Base your answers to questions 1–6 on the information below.
A mass is attached to a spring and moves with simple harmonic motion on a frictionless horizontal surface.
6. If the mass is 48 kg and the spring constant is 12 N/m, what is the period of the oscillation?
F. 8p s H. p s
G. 4p s J. p/2 s

60. Multiple Choice, continued
Chapter 11
Standardized Test Prep
Multiple Choice, continued
Base your answers to questions 7–10 on the information below.
A pendulum bob hangs from a string and moves with simple harmonic motion.
7. What is the restoring force in the pendulum?
A. the total weight of the bob
B. the component of the bob’s weight tangent to the motion of the bob
C. the component of the bob’s weight perpendicular to the motion of the bob
D. the elastic force of the stretched string

61. Multiple Choice, continued
Chapter 11
Standardized Test Prep
Multiple Choice, continued
Base your answers to questions 7–10 on the information below.
A pendulum bob hangs from a string and moves with simple harmonic motion.
7. What is the restoring force in the pendulum?
A. the total weight of the bob
B. the component of the bob’s weight tangent to the motion of the bob
C. the component of the bob’s weight perpendicular to the motion of the bob
D. the elastic force of the stretched string

62. Multiple Choice, continued
Chapter 11
Standardized Test Prep
Multiple Choice, continued
Base your answers to questions 7–10 on the information below.
A pendulum bob hangs from a string and moves with simple harmonic motion.
8. Which of the following does not affect the
period of the pendulum?
F. the length of the string
G. the mass of the pendulum bob
H. the free-fall acceleration at the pendulum’s location
J. All of the above affect the period.

63. Multiple Choice, continued
Chapter 11
Standardized Test Prep
Multiple Choice, continued
Base your answers to questions 7–10 on the information below.
A pendulum bob hangs from a string and moves with simple harmonic motion.
8. Which of the following does not affect the
period of the pendulum?
F. the length of the string
G. the mass of the pendulum bob
H. the free-fall acceleration at the pendulum’s location
J. All of the above affect the period.

64. Multiple Choice, continued
Chapter 11
Standardized Test Prep
Multiple Choice, continued
Base your answers to questions 7–10 on the information below.
A pendulum bob hangs from a string and moves with simple harmonic motion.
9. If the pendulum completes exactly 12
cycles in 2.0 min, what is the frequency of
the pendulum?
A Hz
B Hz
C. 6.0 Hz
D. 10 Hz

65. Multiple Choice, continued
Chapter 11
Standardized Test Prep
Multiple Choice, continued
Base your answers to questions 7–10 on the information below.
A pendulum bob hangs from a string and moves with simple harmonic motion.
9. If the pendulum completes exactly 12
cycles in 2.0 min, what is the frequency of
the pendulum?
A Hz
B Hz
C. 6.0 Hz
D. 10 Hz

66. Multiple Choice, continued
Chapter 11
Standardized Test Prep
Multiple Choice, continued
Base your answers to questions 7–10 on the information below.
A pendulum bob hangs from a string and moves with simple harmonic motion.
10. If the pendulum’s length is 2.00 m and
ag = 9.80 m/s2, how many complete
oscillations does the pendulum make in
5.00 min?
F H. 106
G J. 239

67. Multiple Choice, continued
Chapter 11
Standardized Test Prep
Multiple Choice, continued
Base your answers to questions 7–10 on the information below.
A pendulum bob hangs from a string and moves with simple harmonic motion.
10. If the pendulum’s length is 2.00 m and
ag = 9.80 m/s2, how many complete
oscillations does the pendulum make in
5.00 min?
F H. 106
G J. 239

68. Multiple Choice, continued
Chapter 11
Standardized Test Prep
Multiple Choice, continued
Base your answers to questions 11–13 on the graph.
11. What kind of wave does this graph represent?
A. transverse wave C. electromagnetic wave
B. longitudinal wave D. pulse wave

69. Multiple Choice, continued
Chapter 11
Standardized Test Prep
Multiple Choice, continued
Base your answers to questions 11–13 on the graph.
11. What kind of wave does this graph represent?
A. transverse wave C. electromagnetic wave
B. longitudinal wave D. pulse wave

70. Multiple Choice, continued
Chapter 11
Standardized Test Prep
Multiple Choice, continued
Base your answers to questions 11–13 on the graph.
12. Which letter on the graph represents wavelength?
F. A H. C
G. B J. D

71. Multiple Choice, continued
Chapter 11
Standardized Test Prep
Multiple Choice, continued
Base your answers to questions 11–13 on the graph.
12. Which letter on the graph represents wavelength?
F. A H. C
G. B J. D

72. Multiple Choice, continued
Chapter 11
Standardized Test Prep
Multiple Choice, continued
Base your answers to questions 11–13 on the graph.
13. Which letter on the graph is used for a trough?
A. A C. C
B. B D. D

73. Multiple Choice, continued
Chapter 11
Standardized Test Prep
Multiple Choice, continued
Base your answers to questions 11–13 on the graph.
13. Which letter on the graph is used for a trough?
A. A C. C
B. B D. D

74. Multiple Choice, continued
Chapter 11
Standardized Test Prep
Multiple Choice, continued
Base your answers to questions 14–15 on the passage.
A wave with an amplitude of 0.75 m has the same wavelength as a second wave with an amplitude of
0.53 m. The two waves interfere.
14. What is the amplitude of the resultant wave if the interference is constructive?
F m
G m
H m
J m

75. Multiple Choice, continued
Chapter 11
Standardized Test Prep
Multiple Choice, continued
Base your answers to questions 14–15 on the passage.
A wave with an amplitude of 0.75 m has the same wavelength as a second wave with an amplitude of
0.53 m. The two waves interfere.
14. What is the amplitude of the resultant wave if the interference is constructive?
F m
G m
H m
J m

76. Multiple Choice, continued
Chapter 11
Standardized Test Prep
Multiple Choice, continued
Base your answers to questions 14–15 on the passage.
A wave with an amplitude of 0.75 m has the same wavelength as a second wave with an amplitude of
0.53 m. The two waves interfere.
15. What is the amplitude of the resultant wave if the interference is destructive?
A m
B m
C m
D m

77. Multiple Choice, continued
Chapter 11
Standardized Test Prep
Multiple Choice, continued
Base your answers to questions 14–15 on the passage.
A wave with an amplitude of 0.75 m has the same wavelength as a second wave with an amplitude of
0.53 m. The two waves interfere.
15. What is the amplitude of the resultant wave if the interference is destructive?
A m
B m
C m
D m

78. Multiple Choice, continued
Chapter 11
Standardized Test Prep
Multiple Choice, continued
16. Two successive crests of a transverse wave 1.20 m apart. Eight crests pass a given point 12.0 s. What is the wave speed?
F m/s
G m/s
H m/s
J m/s

79. Multiple Choice, continued
Chapter 11
Standardized Test Prep
Multiple Choice, continued
16. Two successive crests of a transverse wave 1.20 m apart. Eight crests pass a given point 12.0 s. What is the wave speed?
F m/s
G m/s
H m/s
J m/s

80. Chapter 11 Short Response
Standardized Test Prep
Short Response
17. Green light has a wavelength of 5.20  10–7 m and a speed in air of 3.00  108 m/s. Calculate the frequency and the period of the light.

81. Chapter 11 Short Response
Standardized Test Prep
Short Response
17. Green light has a wavelength of 5.20  10–7 m and a speed in air of 3.00  108 m/s. Calculate the frequency and the period of the light.
Answer: 5.77  1014 Hz, 1.73  10–15 s

82. Short Response, continued
Chapter 11
Standardized Test Prep
Short Response, continued
18. What kind of wave does not need a medium through which to travel?

83. Short Response, continued
Chapter 11
Standardized Test Prep
Short Response, continued
18. What kind of wave does not need a medium through which to travel?
Answer: electromagnetic waves

84. Short Response, continued
Chapter 11
Standardized Test Prep
Short Response, continued
19. List three wavelengths that could form standing waves on a 2.0 m string that is fixed at both ends.

85. Short Response, continued
Chapter 11
Standardized Test Prep
Short Response, continued
19. List three wavelengths that could form standing waves on a 2.0 m string that is fixed at both ends.
Answer: Possible correct answers include 4.0 m, 2.0 m, 1.3 m, 1.0 m, or other wavelengths such that nl = 4.0 m (where n is a positive integer).

86. Chapter 11 Extended Response
Standardized Test Prep
Extended Response
20. A visitor to a lighthouse wishes to find out the height of the tower. The visitor ties a spool of thread to a small rock to make a simple pendulum. Then, the visitor hangs the pendulum down a spiral staircase in the center of the tower. The period of oscillation is 9.49 s. What is the height of the tower? Show all of your work.

87. Chapter 11 Extended Response
Standardized Test Prep
Extended Response
20. A visitor to a lighthouse wishes to find out the height of the tower. The visitor ties a spool of thread to a small rock to make a simple pendulum. Then, the visitor hangs the pendulum down a spiral staircase in the center of the tower. The period of oscillation is 9.49 s. What is the height of the tower? Show all of your work.
Answer: 22.4 m

88. Extended Response, continued
Chapter 11
Standardized Test Prep
Extended Response, continued
21. A harmonic wave is traveling along a rope. The oscillator that generates the wave completes 40.0 vibrations in 30.0 s. A given crest of the wave travels 425 cm along the rope in a period of 10.0 s. What is the wavelength? Show all of your work.

89. Extended Response, continued
Chapter 11
Standardized Test Prep
Extended Response, continued
21. A harmonic wave is traveling along a rope. The oscillator that generates the wave completes 40.0 vibrations in 30.0 s. A given crest of the wave travels 425 cm along the rope in a period of 10.0 s. What is the wavelength? Show all of your work.
Answer: m

90. Section 1 Simple Harmonic Motion
Chapter 11
Hooke’s Law

91. Section 3 Properties of Waves
Chapter 11
Transverse Waves

92. Section 3 Properties of Waves
Chapter 11
Longitudinal Waves

93. Constructive Interference
Section 4 Wave Interactions
Chapter 11
Constructive Interference

94. Destructive Interference
Section 4 Wave Interactions
Chapter 11
Destructive Interference

95. Reflection of a Pulse Wave
Section 4 Wave Interactions
Chapter 11
Reflection of a Pulse Wave