Simple Harmonic Motion

1
Simple Harmonic Motion

• Vibration / oscillation motion which
• Regularly Repeats itself
• Back and forth
• Cycle complete to-and-fro motion
• Cyclefrom peak to trough back to peak or
• From trough to peak back to trough

2
Simple Harmonic Motion

• Vibration / oscillation motion which
• Regularly Repeats itself
• Back and forth
• Cycle complete to-and-fro motion
• Cyclefrom peak to trough back to peak or
• From trough to peak back to trough

3
Simple Harmonic Motion

• Vibration / oscillation motion which
• Regularly Repeats itself
• Back and forth
• Cycle complete to-and-fro motion
• Cyclefrom peak to trough back to peak or
• From trough to peak back to trough

4
Simple Harmonic Motion

• Vibration / oscillation motion which
• Regularly Repeats itself
• Back and forth
• Cycle complete to-and-fro motion
• Cyclefrom peak to trough back to peak or
• From trough to peak back to trough

5
Simple Harmonic Motion

• Vibration / oscillation motion which
• Regularly Repeats itself
• Back and forth
• Cycle complete to-and-fro motion
• Cyclefrom peak to trough back to peak or
• From trough to peak back to trough

6
Simple Harmonic Motion

• Vibration / oscillation motion which
• Regularly Repeats itself
• Back and forth
• Cycle complete to-and-fro motion
• Cyclefrom peak to trough back to peak or
• From trough to peak back to trough

7
Simple Harmonic Motion

• Vibration / oscillation motion which
• Regularly Repeats itself
• Back and forth
• Cycle complete to-and-fro motion
• Cyclefrom peak to trough back to peak or
• From trough to peak back to trough

8
Simple Harmonic Motion

• Vibration / oscillation motion which
• Regularly Repeats itself
• Back and forth
• Cycle complete to-and-fro motion
• Cyclefrom peak to trough back to peak or
• From trough to peak back to trough

9
Simple Harmonic Motion

• Period- the time it takes for one complete
• cycle
• Frequency- The number of cycles completed per
  second
• Frequency-measured in Hertz- cycles per sec.
• Frequency Units- 1/s or s-1
• f1/T
• T1/f

10
Simple Harmonic Motion

• Period- the time it takes for one complete
• cycle
• Frequency- The number of cycles completed per
  second
• Frequency-measured in Hertz- cycles per sec.
• Frequency Units- 1/s or s-1
• f1/T
• T1/f

11
Simple Harmonic Motion

• Period- the time it takes for one complete
• cycle
• Frequency- The number of cycles completed per
  second
• Frequency-measured in Hertz- cycles per sec.
• Frequency Units- 1/s or s-1
• f1/T
• T1/f

12
Simple Harmonic Motion

• Period- the time it takes for one complete
• cycle
• Frequency- The number of cycles completed per
  second
• Frequency-measured in Hertz- cycles per sec.
• Frequency Units- 1/s or s-1
• f1/T
• T1/f

13
Simple Harmonic Motion

• Period- the time it takes for one complete
• cycle
• Frequency- The number of cycles completed per
  second
• Frequency-measured in Hertz- cycles per sec.
• Frequency Units- 1/s or s-1
• f1/T
• T1/f

14
Simple Harmonic Motion

• Period- the time it takes for one complete
• cycle
• Frequency- The number of cycles completed per
  second
• Frequency-measured in Hertz- cycles per sec.
• Frequency Units- 1/s or s-1
• f1/T
• T1/f

15
Simple Harmonic Motion

• Period- the time it takes for one complete
• cycle
• Frequency- The number of cycles completed per
  second
• Frequency-measured in Hertz- cycles per sec.
• Frequency Units- 1/s or s-1
• f1/T
• T1/f

16
Simple Harmonic Motion

• Period- the time it takes for one complete
• cycle
• Frequency- The number of cycles completed per
  second
• Frequency-measured in Hertz- cycles per sec.
• Frequency Units- 1/s or s-1
• f1/T
• T1/f

17
Simple Harmonic Motion
ms
18
Simple Harmonic Motion
ms
19
Simple Harmonic Motion
0 ms 3.1 ms 6.3ms
9.6ms
ms
20
Simple Harmonic Motion
0 ms 3.1 ms 6.3ms
9.6ms
ms
21
Simple Harmonic Motion
0 ms 3.1 ms 6.3ms
9.6ms
ms
22
Simple Harmonic Motion
0 ms 3.1 ms 6.3ms
9.6ms
ms
23
Simple Harmonic Motion
0 ms 3.1 ms 6.3ms
9.6ms
ms
Frequency cycles per second
24
Simple Harmonic Motion
0 ms 3.1 ms 6.3ms
9.6ms
ms
Frequency cycles per second 3 cycles /
25
Simple Harmonic Motion
0 ms 3.1 ms 6.3ms
9.6ms
ms
Frequency cycles per second 3 cycles / 9.6 ms
3 cycles /(.0096s)
26
Simple Harmonic Motion
0 ms 3.1 ms 6.3ms
9.6ms
ms
Frequency cycles per second 3 cycles / 9.6 ms
3 cycles /(.0096s) 312.5 Hz
27
Simple Harmonic Motion
0 ms 3.1 ms 6.3ms
9.6ms
ms
Frequency cycles per second 3 cycles / 9.6 ms
3 cycles /(.0096s) 312.5 Hz Period 1 / f
28
Simple Harmonic Motion
0 ms 3.1 ms 6.3ms
9.6ms
ms
Frequency cycles per second 3 cycles / 9.6 ms
3 cycles /(.0096s) 312.5 Hz Period 1 / f
1 / 312.5 s .0032 s or 3.2 ms on average
29
Simple Harmonic Motion
0 ms 3.1 ms 6.3ms
9.6ms
ms
Frequency cycles per second 3 cycles / 9.6 ms
3 cycles /(.0096s) 312.5 Hz Period 1 / f
1 / 312.5 s .0032 s or 3.2 ms on average
30
Period of oscillation of a Spring Mass
SystemPeriod of oscillation of Pendulum Mass
System

• Spring
• T2p m
• k
• Dependent on mass and inversely related to the
  spring constant
• Pendulum
• T2p l
• g
• Dependent on length and inversely related to the
  acceleration due to gravity

31
Period of oscillation of a Spring Mass
SystemPeriod of oscillation of Pendulum Mass
System

• Spring
• T2p m
• k
• Dependent on mass and inversely related to the
  spring constant
• Pendulum
• T2p l
• g
• Dependent on length and inversely related to the
  acceleration due to gravity

32
Period of oscillation of a Spring Mass
SystemPeriod of oscillation of Pendulum Mass
System

• Spring
• T2p m
• k
• Dependent on mass and inversely related to the
  spring constant
• Pendulum
• T2p l
• g
• Dependent on length and inversely related to the
  acceleration due to gravity

33
Period of oscillation of a Spring Mass
SystemPeriod of oscillation of Pendulum Mass
System

• Spring
• T2p m
• k
• Dependent on mass and inversely related to the
  spring constant
• Pendulum
• T2p l
• g
• Dependent on length and inversely related to the
  acceleration due to gravity

34
Period of oscillation of a Spring Mass
SystemPeriod of oscillation of Pendulum Mass
System

• Spring
• T2p m
• k
• Dependent on mass and inversely related to the
  spring constant
• Pendulum
• T2p l
• g
• Dependent on length and inversely related to the
  acceleration due to gravity

35
Period of oscillation of a Spring Mass
SystemPeriod of oscillation of Pendulum Mass
System

• Spring
• T2p m
• k
• Dependent on mass and inversely related to the
  spring constant
• Pendulum
• T2p l
• g
• Dependent on length and inversely related to the
  acceleration due to gravity

36
Period of oscillation of a Spring Mass
SystemPeriod of oscillation of Pendulum Mass
System

• Spring
• T2p m
• k
• Dependent on mass and inversely related to the
  spring constant
• Pendulum
• T2p l
• g
• Dependent on length and inversely related to the
  acceleration due to gravity

37
Natural Frequency Forced Vibration-Resonance

• The frequency that a system occurs when a force
  is applied to it.
• A Driving Force is a force that is applied over
  and over again.

38
Natural Frequency Forced Vibration-Resonance

• The frequency that a system acquires when a
  force is applied to it.
• A Driving Force is a force that is applied over
  and over again.

39
Natural Frequency Forced Vibration-Resonance

• The frequency that a system acquires when a
  force is applied to it.
• A Driving Force is a force that is applied over
  and over again.
• Resonance occurs when the driving force is
  applied at the natural frequency or multiples of
  the natural frequency

40
Natural Frequency Forced Vibration-Resonance

• The frequency that a system acquires when a
  force is applied to it.
• A Driving Force is a force that is applied over
  and over again.
• Resonance occurs when the driving force is
  applied at the natural frequency or multiples of
  the natural frequency
• Resonance produces large amplitude standing waves

41
Natural Frequency Forced Vibration-Resonance

• The frequency that a system acquires when a
  force is applied to it.
• A Driving Force is a force that is applied over
  and over again.
• Resonance occurs when the driving force is
  applied at the natural frequency or multiples of
  the natural frequency
• Resonance produces large amplitude standing waves

42
Natural Frequency Forced Vibration-Resonance

• Resonance caused the Tacoma Narrows Bridge to
  collapse
• Resonance can cause a wine glass to break
• Resonance can is used in string instruments, open
  end wind instruments, and closed end tube wind
  instruments

43
Standing Waves

• Nodes points of destructive interference
• Antinodes points of constructive interference
• Standing waves are produced at natural
  frequencies or resonant frequencies.

44
Standing Waves strings

• L n l / 2
• L the length of a string
• Lambda equals the wavelength
• n an interger
• n 1 fundamental frequency
• n 2 second harmonic
• n 3 third hamonic

45
Standing Waves Open Springs continued.

• Nodes are found at the fixed ends.
• Antinodes are not possible at the fixed ends
• The velocity on a string is directly related to
  its tension and inversely related to the mass per
  unit length.

46
Standing waves open end tubes

• Antinodes are possible at the open ends
• Ln l / 2
• Llength of the tube
• lambda wavelength
• n 1 fundamental frequency
• n 2 2nd harmonic
• n 3 3rd harmonic

47
Standing waves open end tubes

• Antinodes are possible at the open ends
• Ln l / 2
• Llength of the tube
• lambda wavelength
• n 1 fundamental frequency
• n 2 2nd harmonic
• n 3 3rd harmonic

48
Standing waves open end tubes

• Antinodes are possible at the open ends
• Ln l / 2
• Llength of the tube
• lambda wavelength
• n 1 fundamental frequency
• n 2 2nd harmonic
• n 3 3rd harmonic

49
Standing waves open end tubes

• Antinodes are possible at the open ends
• Ln l / 2
• Llength of the tube
• lambda wavelength
• n 1 fundamental frequency
• n 2 2nd harmonic
• n 3 3rd harmonic

50
Standing waves open end tubes

• Antinodes are possible at the open ends
• Ln l / 2
• Llength of the tube
• lambda wavelength
• n 1 fundamental frequency
• n 2 2nd harmonic
• n 3 3rd harmonic

51
Standing waves open end tubes

• Antinodes are possible at the open ends
• Ln l / 2
• Llength of the tube
• lambda wavelength
• n 1 fundamental frequency
• n 2 2nd harmonic
• n 3 3rd harmonic

52
Standing waves open end tubes

• Antinodes are possible at the open ends
• Ln l / 2
• Llength of the tube
• lambda wavelength
• n 1 fundamental frequency
• n 2 2nd harmonic
• n 3 3rd harmonic

53
Standing waves open end tubes

• Antinodes are possible at the open ends
• Ln l / 2
• Llength of the tube
• lambda wavelength
• n 1 fundamental frequency
• n 2 2nd harmonic
• n 3 3rd harmonic

54
Standing waves open end tubes

• v speed of sound
• v (331 .6 T) m / s

55
Standing waves closed end tubes

• L l / 4
• L length of the tube
• lamda wavelength
• antinodes are possible at the open end.
• nodes are possible at the closed end.
• Only odd harmonics are possible.

56
Standing waves closed end tubes

• L lambda / 4
• L length of the tube
• lamda wavelength
• antinodes are possible at the open end.
• nodes are possible at the closed end.
• Only odd harmonics are possible.

57
Standing waves closed end tubes

• L lambda / 4
• L length of the tube
• lamda wavelength
• antinodes are possible at the open end.
• nodes are possible at the closed end.
• Only odd harmonics are possible.

58
Standing waves closed end tubes

• L lambda / 4
• L length of the tube
• lamda wavelength
• antinodes are possible at the open end.
• nodes are possible at the closed end.
• Only odd harmonics are possible.

59
Standing waves closed end tubes

• L lambda / 4
• L length of the tube
• lamda wavelength
• antinodes are possible at the open end.
• nodes are possible at the closed end.
• Only odd harmonics are possible.

60
Standing waves closed end tubes

• L lambda / 4
• L length of the tube
• lamda wavelength
• antinodes are possible at the open end.
• nodes are possible at the closed end.
• Only odd harmonics are possible.

1
61
Standing waves closed end tubes

• L lambda / 4
• L length of the tube
• lamda wavelength
• antinodes are possible at the open end.
• nodes are possible at the closed end.
• Only odd harmonics are possible.

3
1
62
Standing waves closed end tubes

• L lambda / 4
• L length of the tube
• lamda wavelength
• antinodes are possible at the open end.
• nodes are possible at the closed end.
• Only odd harmonics are possible.

3
5
1
63
Beats

• The rising and falling of sound intensity is
  known as beats
• The beat frequency tells you how many cycles per
  second the source frequency is different than the
  standard frequency.
• The beat frequency does not tell you if the
  source frequency is higher or lower than the
  standard.

64
Beats
65
Doppler Effect

• ffo ( v - vo )
• ( v - vs)
• vo velocity of the observer
• vs velocity of the source.
• vo observer towards source f increases WHY?
• vo - source towards observer-f increases WHY?

66
Doppler Effect

• ffo ( v - vo )
• ( v - vs)
• vo observer towards source f increases WHY?
• Multiply be a larger Numerator Higher f
• vo - source towards observer-f increases WHY?
• Divide by a smaller Denominator Higher f

67
Wave Motion

• Matter is not carried in mechanical waves.
• Energy is carried by mechanical waves.
• A wave has a velocity equal to the product of..
• its frequency and wavelength. V f lamda

68
Wave Motion

• Matter is not carried in mechanical waves.
• Energy is carried by mechanical waves.
• A wave has a velocity equal to the product of..
• its frequency and wavelength. V f lamda

69
Wave Motion

• Matter is not carried in mechanical waves.
• Energy is carried by mechanical waves.
• A wave has a velocity equal to the product of..
• its frequency and wavelength. V f lamda

70
Wave Motion

• Matter is not carried in mechanical waves.
• Energy is carried by mechanical waves.
• A wave has a velocity equal to the product of..
• its frequency and wavelength. V f l

71
Wave Properties

• Amplitudemaximum height relative to
• The equilibrium
• Wavelengthdistance between crests
• Frequency the number of crests which pass a
  given pt per second cycle per sec 1 Hz

72
Wave Properties

• Amplitudemaximum height relative to
• The equilibrium
• Wavelengthdistance between crests
• Frequency the number of crests which pass a
  given pt per second cycle per sec 1 Hz

73
Wave Properties

• Amplitudemaximum height relative to
• The equilibrium
• Wavelengthdistance between crests
• Frequency the number of crests which pass a
  given pt per second cycle per sec 1 Hz

74
Wave Properties

• Amplitudemaximum height relative to
• The equilibrium
• Wavelengthdistance between crests
• Frequency the number of crests which pass a
  given pt per second cycle per sec 1 Hz

75
Wave Properties

• Amplitudemaximum height relative to
• The equilibrium
• Wavelengthdistance between crests
• Frequency the number of crests which pass a
  given point per second cycle per sec 1 Hz

76
Wave Properties

• Amplitudemaximum height relative to
• The equilibrium
• Wavelengthdistance between crests
• Frequency the number of crests which pass a
  given pt per second cycle per sec 1 Hz

77
Velocity of a Wave on a string

• v FT
• (m/l)
• FT is the equal to the
• Tension in the string.
• m / L is the
• The mass per unit length of the string.

78
Velocity of a Wave on a string

• v FT
• (m/l)
• FT is the equal to the
• Tension in the string.
• m / L is the
• The mass per unit length of the string.

79
Velocity of a Wave on a string

• v FT
• (m/l)
• FT Tension in the string.
• m / L is the
• The mass per unit length of the string.

80
Velocity of a Wave on a string

• v FT
• (m/l)
• FT Tension in the string.
• m / L is the
• The mass per unit length of the string.

81
Velocity of a Wave on a string

• v FT
• (m/l)
• FT Tension in the string.
• m / L is the
• The mass per unit length of the string.

82
Velocity of a Wave on a string

• v FT
• (m/l)
• FT Tension in the string.
• m / L is the
• The mass per unit length of the string or..

83
Velocity of a Wave on a string

• v FT
• (m/l)
• FT Tension in the string.
• m / L is the
• The mass per unit length of the string or..
• Linear Density in kg/m

84
Types of waves

• transverse..
• Oscillation is perpendicular to the wave motion
• (Electromagnetic waves are transverse waves

85
Types of waves

• Longitudinal
• Oscillation is parallel to the wave motion
• (sound waves are longitudinal waves )

86
Types of waves

• Longitudinal
• Oscillation is parallel to the wave motion
• (sound waves are longitudinal waves )

87
Speed of waves

• The speed of a wave is directly related to the..
• Elastic force factor and.
• The interia factor (density of the medium

88
Speed of waves

• The speed of a wave is directly related to the..
• Elastic force factor and.
• The interia factor (density of the medium

89
Wave intensity

• Intensity is
• The power transported across a unit area
  perpendicular the energy flow of a wave.
• Intensity energy / time divided by area
• Intensity power / area
• Intensity Watt / meters squared.
• The intensity of a wave decreases by 1/r2

90
Wave intensity

• Intensity is
• The power transported across a unit area
  perpendicular the energy flow of a wave.
• Intensity energy / time divided by area
• Intensity power / area
• Intensity Watt / meters squared.
• The intensity of a wave decreases by 1/r2

91
Wave intensity

• Intensity is
• The power transported across a unit area
  perpendicular the energy flow of a wave.
• Intensity energy / time divided by area
• Intensity power / area
• Intensity Watt / meters squared.
• The intensity of a wave decreases by 1/r2

92
Wave intensity

• Intensity is
• The power transported across a unit area
  perpendicular the energy flow of a wave.
• Intensity energy / time divided by area
• Intensity power / area
• Intensity Watt / meters squared.
• The intensity of a wave decreases by 1/r2

93
Wave intensity

• Intensity is
• The power transported across a unit area
  perpendicular the energy flow of a wave.
• Intensity energy / time divided by area
• Intensity power / area
• Intensity Watt / meters squared.
• The intensity of a wave decreases by 1/r2

94
Wave intensity

• Intensity is
• The power transported across a unit area
  perpendicular the energy flow of a wave.
• Intensity energy / time divided by area
• Intensity power / area
• Intensity Watt / meters squared.
• The intensity of a wave decreases by 1/r2

95
Decibels

• Relative measure of the perceived loudness of a
  sound wave
• Decibels are based on a logarithmic scale
• dB10 log ( Intensity of the sound wave
  )
• ( Threshold of Human Hearing
  Intensity )
• Threshold of Hearing 1x10-12 W/m2
• What is the intensity of a 75 dB sound wave?
• 75dB 10 log ( I / Io)
• 7.5 log ( I / Io)
• 7.5 log I log Io
• 7.5 log I log (1 x10-12 W/m2)
• 7.5 log I (-12)
• 7.5 12 log I
• -4.5 log I
• 3.16 x10-5 W / m2 I

96
Decibels

• Relative measure of the perceived loudness of a
  sound wave
• Decibels are based on a logarithmic scale
• dB10 log ( Intensity of the sound wave
  )
• ( Threshold of Human Hearing
  Intensity )
• Threshold of Hearing 1x10-12 W/m2
• What is the intensity of a 75 dB sound wave?
• 75dB 10 log ( I / Io)
• 7.5 log ( I / Io)
• 7.5 log I log Io
• 7.5 log I log (1 x10-12 W/m2)
• 7.5 log I (-12)
• 7.5 12 log I
• -4.5 log I
• 3.16 x10-5 W / m2 I

97
Decibels

• Relative measure of the perceived loudness of a
  sound wave
• Decibels are based on a logarithmic scale
• dB10 log ( Intensity of the sound wave
  )
• ( Threshold of Human Hearing
  Intensity )
• Threshold of Hearing 1x10-12 W/m2
• What is the intensity of a 75 dB sound wave?
• 75dB 10 log ( I / Io)
• 7.5 log ( I / Io)
• 7.5 log I log Io
• 7.5 log I log (1 x10-12 W/m2)
• 7.5 log I (-12)
• 7.5 12 log I
• -4.5 log I
• 3.16 x10-5 W / m2 I

98
Decibels

• Relative measure of the perceived loudness of a
  sound wave
• Decibels are based on a logarithmic scale
• dB10 log ( Intensity of the sound wave
  )
• ( Threshold of Human Hearing
  Intensity )
• Threshold of Hearing 1x10-12 W/m2
• What is the intensity of a 75 dB sound wave?
• 75dB 10 log ( I / Io)
• 7.5 log ( I / Io)
• 7.5 log I log Io
• 7.5 log I log (1 x10-12 W/m2)
• 7.5 log I (-12)
• 7.5 12 log I
• -4.5 log I
• 3.16 x10-5 W / m2 I

99
Decibels

• Relative measure of the perceived loudness of a
  sound wave
• Decibels are based on a logarithmic scale
• dB10 log ( Intensity of the sound wave
  )
• ( Threshold of Human Hearing
  Intensity )
• Threshold of Hearing 1x10-12 W/m2
• What is the intensity of a 75 dB sound wave?
• 75dB 10 log ( I / Io)
• 7.5 log ( I / Io)
• 7.5 log I log Io
• 7.5 log I log (1 x10-12 W/m2)
• 7.5 log I (-12)
• 7.5 12 log I
• -4.5 log I
• 3.16 x10-5 W / m2 I

100
Decibels

• Relative measure of the perceived loudness of a
  sound wave
• Decibels are based on a logarithmic scale
• dB10 log ( Intensity of the sound wave
  )
• ( Threshold of Human Hearing
  Intensity )
• Threshold of Hearing 1x10-12 W/m2
• What is the intensity of a 75 dB sound wave?
• 75dB 10 log ( I / Io)
• 7.5 log ( I / Io)
• 7.5 log I log Io
• 7.5 log I log (1 x10-12 W/m2)
• 7.5 log I (-12)
• 7.5 12 log I
• -4.5 log I
• 3.16 x10-5 W / m2 I

101
Decibels

• Relative measure of the perceived loudness of a
  sound wave
• Decibels are based on a logarithmic scale
• dB10 log ( Intensity of the sound wave
  )
• ( Threshold of Human Hearing
  Intensity )
• Threshold of Hearing 1x10-12 W/m2
• What is the intensity of a 75 dB sound wave?
• 75dB 10 log ( I / Io)
• 7.5 log ( I / Io)
• 7.5 log I log Io
• 7.5 log I log (1 x10-12 W/m2)
• 7.5 log I (-12)
• 7.5 12 log I
• -4.5 log I
• 3.16 x10-5 W / m2 I

102
Decibels

• Relative measure of the perceived loudness of a
  sound wave
• Decibels are based on a logarithmic scale
• dB10 log ( Intensity of the sound wave
  )
• ( Threshold of Human Hearing
  Intensity )
• Threshold of Hearing 1x10-12 W/m2
• What is the intensity of a 75 dB sound wave?
• 75dB 10 log ( I / Io)
• 7.5 log ( I / Io)
• 7.5 log I log Io
• 7.5 log I log (1 x10-12 W/m2)
• 7.5 log I (-12)
• 7.5 12 log I
• -4.5 log I
• 3.16 x10-5 W / m2 I

103
Decibels

• Relative measure of the perceived loudness of a
  sound wave
• Decibels are based on a logarithmic scale
• dB10 log ( Intensity of the sound wave
  )
• ( Threshold of Human Hearing
  Intensity )
• Threshold of Hearing 1x10-12 W/m2
• What is the intensity of a 75 dB sound wave?
• 75dB 10 log ( I / Io)
• 7.5 log ( I / Io)
• 7.5 log I log Io
• 7.5 log I log (1 x10-12 W/m2)
• 7.5 log I (-12)
• 7.5 12 log I
• -4.5 log I
• 3.16 x10-5 W / m2 I

104
Decibels

• Relative measure of the perceived loudness of a
  sound wave
• Decibels are based on a logarithmic scale
• dB10 log ( Intensity of the sound wave
  )
• ( Threshold of Human Hearing
  Intensity )
• Threshold of Hearing 1x10-12 W/m2
• What is the intensity of a 75 dB sound wave?
• 75dB 10 log ( I / Io)
• 7.5 log ( I / Io)
• 7.5 log I log Io
• 7.5 log I log (1 x10-12 W/m2)
• 7.5 log I (-12)
• 7.5 12 log I
• -4.5 log I
• 3.16 x10-5 W / m2 I

105
Decibels

• Relative measure of the perceived loudness of a
  sound wave
• Decibels are based on a logarithmic scale
• dB10 log ( Intensity of the sound wave
  )
• ( Threshold of Human Hearing
  Intensity )
• Threshold of Hearing 1x10-12 W/m2
• What is the intensity of a 75 dB sound wave?
• 75dB 10 log ( I / Io)
• 7.5 log ( I / Io)
• 7.5 log I log Io
• 7.5 log I log (1 x10-12 W/m2)
• 7.5 log I (-12)
• 7.5 12 log I
• -4.5 log I
• 3.16 x10-5 W / m2 I

106
Decibels

• Relative measure of the perceived loudness of a
  sound wave
• Decibels are based on a logarithmic scale
• dB10 log ( Intensity of the sound wave
  )
• ( Threshold of Human Hearing
  Intensity )
• Threshold of Hearing 1x10-12 W/m2
• What is the intensity of a 75 dB sound wave?
• 75dB 10 log ( I / Io)
• 7.5 log ( I / Io)
• 7.5 log I log Io
• 7.5 log I log (1 x10-12 W/m2)
• 7.5 log I (-12)
• 7.5 12 log I
• -4.5 log I
• 3.16 x10-5 W / m2 I

107
Decibels

• Relative measure of the perceived loudness of a
  sound wave
• Decibels are based on a logarithmic scale
• dB10 log ( Intensity of the sound wave
  )
• ( Threshold of Human Hearing
  Intensity )
• Threshold of Hearing 1x10-12 W/m2
• What is the intensity of a 75 dB sound wave?
• 75dB 10 log ( I / Io)
• 7.5 log ( I / Io)
• 7.5 log I log Io
• 7.5 log I log (1 x10-12 W/m2)
• 7.5 log I (-12)
• 7.5 12 log I
• -4.5 log I
• 3.16 x10-5 W / m2 I

108
Decibels

• Relative measure of the perceived loudness of a
  sound wave
• Decibels are based on a logarithmic scale
• dB10 log ( Intensity of the sound wave
  )
• ( Threshold of Human Hearing
  Intensity )
• Threshold of Hearing 1x10-12 W/m2
• What is the intensity of a 75 dB sound wave?
• 75dB 10 log ( I / Io)
• 7.5 log ( I / Io)
• 7.5 log I log Io
• 7.5 log I log (1 x10-12 W/m2)
• 7.5 log I (-12)
• 7.5 12 log I
• -4.5 log I
• 3.16 x10-5 W / m2 I

109
Decibels

• Relative measure of the perceived loudness of a
  sound wave
• Decibels are based on a logarithmic scale
• dB10 log ( Intensity of the sound wave
  )
• ( Threshold of Human Hearing
  Intensity )
• Threshold of Hearing 1x10-12 W/m2
• How many times more intense is a 120 dB sound
  wave
• compared to a 80 dB sound wave?
• 120dB 80 dB 40 db
• 40 dB / 10 4
• 104 10,000 times greater

110
Decibels

• Relative measure of the perceived loudness of a
  sound wave
• Decibels are based on a logarithmic scale
• dB10 log ( Intensity of the sound wave
  )
• ( Threshold of Human Hearing
  Intensity )
• Threshold of Hearing 1x10-12 W/m2
• How many times more intense is a 120 dB sound
  wave
• compared to a 80 dB sound wave?
• 120dB 80 dB 40 db
• 40 dB / 10 4
• 104 10,000 times greater

111
Decibels

• Relative measure of the perceived loudness of a
  sound wave
• Decibels are based on a logarithmic scale
• dB10 log ( Intensity of the sound wave
  )
• ( Threshold of Human Hearing
  Intensity )
• Threshold of Hearing 1x10-12 W/m2
• How many times more intense is a 120 dB sound
  wave
• compared to a 80 dB sound wave?
• 120dB 80 dB 40 db
• 40 dB / 10 4
• 104 10,000 times greater

112
Decibels

• Relative measure of the perceived loudness of a
  sound wave
• Decibels are based on a logarithmic scale
• dB10 log ( Intensity of the sound wave
  )
• ( Threshold of Human Hearing
  Intensity )
• Threshold of Hearing 1x10-12 W/m2
• How many times more intense is a 120 dB sound
  wave
• compared to a 80 dB sound wave?
• 120dB 80 dB 40 db
• 40 dB / 10 4
• 104 10,000 times greater

113
Decibels

• Relative measure of the perceived loudness of a
  sound wave
• Decibels are based on a logarithmic scale
• dB10 log ( Intensity of the sound wave
  )
• ( Threshold of Human Hearing
  Intensity )
• Threshold of Hearing 1x10-12 W/m2
• How many times more intense is a 120 dB sound
  wave
• compared to a 80 dB sound wave?
• 120dB 80 dB 40 db
• 40 dB / 10 4
• 104 10,000 times greater

114
Wave Reflection-Fixed end

• A single wave crest which reflects off a fixed
  end will leave as a single wave trough.
• The wave crests puts a force up on the fixed end.
• The fixed puts an equal but opposite force on the
  string which produces an equal but opposite wave
  trough.

115
Wave Reflection-Fixed end

• A single wave crest which reflects off a fixed
  end will leave as a single wave trough.
• The wave crests puts a force up on the fixed end.
• The fixed puts an equal but opposite force on the
  string which produces an equal but opposite wave
  trough.

116
Wave Reflection-Free end

• A single wave peak which reflects off a free end
  will leave as a single wave peak.