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Vibrations and Waves
When you hang a weight on a spring the weight applies a force to the spring and it stretches in direct proportion to the applied force
According to Hookersquos law the amount of stretch (or compression) x is directly proportional to the applied force F
Double the force and you double the stretch triple the force and you get three times the stretch and so on F ~ ∆x
Elasticity
If an elastic material is stretched or compressed more than a certain amount it will not return to its original state
The distance at which permanent distortion occurs is called the elastic limit
Hookersquos law holds only as long as the force does not stretch or compress the material beyond its elastic limit
Elasticity
Free Body Diagrams Revisited
Hookersquos LawSpring force = - (spring constant) (displacement)
Felastic = -kx
Hookersquos LawIf a mass of 055 kg attached to a vertical spring stretches the spring 20 cm from its original equilibrium what is the spring constant
Simple Harmonic MotionVibration about an equilibrium position in
which a restoring force is proportional to the displacement from equilibrium
Simple PendulumsAmplitude
Length
Period
Frequency
Simple Pendulums
Simple PendulumsAt what position in the cycle of a swinging
pendulum is the potential energy of the pendulum at a maximum
Simple Harmonic Motion Calculations
2L
Tg
2m
Tk
For a simple pendulum in simple harmonic motion
For a mass-spring system in simple harmonic motion
WavesMedium ndash a physical environment through
which a disturbance can travel
Mechanical wave ndash a wave that requires a medium to travel through
Examples Non-examples
Transverse Waves
Wave motion is perpendicular to equilibrium
Transverse Waves
Transerve Waves
Longitudinal Waves
Wave motion is parallel to equilibrium
Wave PropertiesPulse wave
A wave that is just one interference ndash no repetition
Reflection
Constructive and Destructive Interference Constructive interference
A superposition of two or more waves in which individual displacements on the same side of the equilibrium position are added together to form the resultant wave
Constructive and Destructive Interference Destructive interference
A superposition of two or more waves in which individual displacements on opposite sides of the equilibrium position are added together to form the resultant wave
Speed of a Wavespeed of a wave = (frequency) (wavelength)
v = f λ
1 A piano emits frequencies that range from a low of about 28 Hz to a high of about 4200 Hz Find the range of wavelengths in air attained by this instrument when the speed of sound in air is 340 ms
2 The red light emitted by a He-Ne laser has a wavelength of 633 nm in air and travels at the speed of light (300 x 108 ms) Find the frequency of the laser light
De Broglie WavesLouis de Broglie suggested that all matter has wavelike characteristics
where h is Planckrsquos constant equal to 663 x 10-
34 Js
This wavelength is too small to notice interference for large objects This idea becomes important when looking all things at the microscopic level
h h
p mv
De Broglie WavesWhat is the wavelength of an electron (mass = 911 x 10macr31 kg) traveling at 531 x 106 ms
When you hang a weight on a spring the weight applies a force to the spring and it stretches in direct proportion to the applied force
According to Hookersquos law the amount of stretch (or compression) x is directly proportional to the applied force F
Double the force and you double the stretch triple the force and you get three times the stretch and so on F ~ ∆x
Elasticity
If an elastic material is stretched or compressed more than a certain amount it will not return to its original state
The distance at which permanent distortion occurs is called the elastic limit
Hookersquos law holds only as long as the force does not stretch or compress the material beyond its elastic limit
Elasticity
Free Body Diagrams Revisited
Hookersquos LawSpring force = - (spring constant) (displacement)
Felastic = -kx
Hookersquos LawIf a mass of 055 kg attached to a vertical spring stretches the spring 20 cm from its original equilibrium what is the spring constant
Simple Harmonic MotionVibration about an equilibrium position in
which a restoring force is proportional to the displacement from equilibrium
Simple PendulumsAmplitude
Length
Period
Frequency
Simple Pendulums
Simple PendulumsAt what position in the cycle of a swinging
pendulum is the potential energy of the pendulum at a maximum
Simple Harmonic Motion Calculations
2L
Tg
2m
Tk
For a simple pendulum in simple harmonic motion
For a mass-spring system in simple harmonic motion
WavesMedium ndash a physical environment through
which a disturbance can travel
Mechanical wave ndash a wave that requires a medium to travel through
Examples Non-examples
Transverse Waves
Wave motion is perpendicular to equilibrium
Transverse Waves
Transerve Waves
Longitudinal Waves
Wave motion is parallel to equilibrium
Wave PropertiesPulse wave
A wave that is just one interference ndash no repetition
Reflection
Constructive and Destructive Interference Constructive interference
A superposition of two or more waves in which individual displacements on the same side of the equilibrium position are added together to form the resultant wave
Constructive and Destructive Interference Destructive interference
A superposition of two or more waves in which individual displacements on opposite sides of the equilibrium position are added together to form the resultant wave
Speed of a Wavespeed of a wave = (frequency) (wavelength)
v = f λ
1 A piano emits frequencies that range from a low of about 28 Hz to a high of about 4200 Hz Find the range of wavelengths in air attained by this instrument when the speed of sound in air is 340 ms
2 The red light emitted by a He-Ne laser has a wavelength of 633 nm in air and travels at the speed of light (300 x 108 ms) Find the frequency of the laser light
De Broglie WavesLouis de Broglie suggested that all matter has wavelike characteristics
where h is Planckrsquos constant equal to 663 x 10-
34 Js
This wavelength is too small to notice interference for large objects This idea becomes important when looking all things at the microscopic level
h h
p mv
De Broglie WavesWhat is the wavelength of an electron (mass = 911 x 10macr31 kg) traveling at 531 x 106 ms
If an elastic material is stretched or compressed more than a certain amount it will not return to its original state
The distance at which permanent distortion occurs is called the elastic limit
Hookersquos law holds only as long as the force does not stretch or compress the material beyond its elastic limit
Elasticity
Free Body Diagrams Revisited
Hookersquos LawSpring force = - (spring constant) (displacement)
Felastic = -kx
Hookersquos LawIf a mass of 055 kg attached to a vertical spring stretches the spring 20 cm from its original equilibrium what is the spring constant
Simple Harmonic MotionVibration about an equilibrium position in
which a restoring force is proportional to the displacement from equilibrium
Simple PendulumsAmplitude
Length
Period
Frequency
Simple Pendulums
Simple PendulumsAt what position in the cycle of a swinging
pendulum is the potential energy of the pendulum at a maximum
Simple Harmonic Motion Calculations
2L
Tg
2m
Tk
For a simple pendulum in simple harmonic motion
For a mass-spring system in simple harmonic motion
WavesMedium ndash a physical environment through
which a disturbance can travel
Mechanical wave ndash a wave that requires a medium to travel through
Examples Non-examples
Transverse Waves
Wave motion is perpendicular to equilibrium
Transverse Waves
Transerve Waves
Longitudinal Waves
Wave motion is parallel to equilibrium
Wave PropertiesPulse wave
A wave that is just one interference ndash no repetition
Reflection
Constructive and Destructive Interference Constructive interference
A superposition of two or more waves in which individual displacements on the same side of the equilibrium position are added together to form the resultant wave
Constructive and Destructive Interference Destructive interference
A superposition of two or more waves in which individual displacements on opposite sides of the equilibrium position are added together to form the resultant wave
Speed of a Wavespeed of a wave = (frequency) (wavelength)
v = f λ
1 A piano emits frequencies that range from a low of about 28 Hz to a high of about 4200 Hz Find the range of wavelengths in air attained by this instrument when the speed of sound in air is 340 ms
2 The red light emitted by a He-Ne laser has a wavelength of 633 nm in air and travels at the speed of light (300 x 108 ms) Find the frequency of the laser light
De Broglie WavesLouis de Broglie suggested that all matter has wavelike characteristics
where h is Planckrsquos constant equal to 663 x 10-
34 Js
This wavelength is too small to notice interference for large objects This idea becomes important when looking all things at the microscopic level
h h
p mv
De Broglie WavesWhat is the wavelength of an electron (mass = 911 x 10macr31 kg) traveling at 531 x 106 ms
Free Body Diagrams Revisited
Hookersquos LawSpring force = - (spring constant) (displacement)
Felastic = -kx
Hookersquos LawIf a mass of 055 kg attached to a vertical spring stretches the spring 20 cm from its original equilibrium what is the spring constant
Simple Harmonic MotionVibration about an equilibrium position in
which a restoring force is proportional to the displacement from equilibrium
Simple PendulumsAmplitude
Length
Period
Frequency
Simple Pendulums
Simple PendulumsAt what position in the cycle of a swinging
pendulum is the potential energy of the pendulum at a maximum
Simple Harmonic Motion Calculations
2L
Tg
2m
Tk
For a simple pendulum in simple harmonic motion
For a mass-spring system in simple harmonic motion
WavesMedium ndash a physical environment through
which a disturbance can travel
Mechanical wave ndash a wave that requires a medium to travel through
Examples Non-examples
Transverse Waves
Wave motion is perpendicular to equilibrium
Transverse Waves
Transerve Waves
Longitudinal Waves
Wave motion is parallel to equilibrium
Wave PropertiesPulse wave
A wave that is just one interference ndash no repetition
Reflection
Constructive and Destructive Interference Constructive interference
A superposition of two or more waves in which individual displacements on the same side of the equilibrium position are added together to form the resultant wave
Constructive and Destructive Interference Destructive interference
A superposition of two or more waves in which individual displacements on opposite sides of the equilibrium position are added together to form the resultant wave
Speed of a Wavespeed of a wave = (frequency) (wavelength)
v = f λ
1 A piano emits frequencies that range from a low of about 28 Hz to a high of about 4200 Hz Find the range of wavelengths in air attained by this instrument when the speed of sound in air is 340 ms
2 The red light emitted by a He-Ne laser has a wavelength of 633 nm in air and travels at the speed of light (300 x 108 ms) Find the frequency of the laser light
De Broglie WavesLouis de Broglie suggested that all matter has wavelike characteristics
where h is Planckrsquos constant equal to 663 x 10-
34 Js
This wavelength is too small to notice interference for large objects This idea becomes important when looking all things at the microscopic level
h h
p mv
De Broglie WavesWhat is the wavelength of an electron (mass = 911 x 10macr31 kg) traveling at 531 x 106 ms
Hookersquos LawSpring force = - (spring constant) (displacement)
Felastic = -kx
Hookersquos LawIf a mass of 055 kg attached to a vertical spring stretches the spring 20 cm from its original equilibrium what is the spring constant
Simple Harmonic MotionVibration about an equilibrium position in
which a restoring force is proportional to the displacement from equilibrium
Simple PendulumsAmplitude
Length
Period
Frequency
Simple Pendulums
Simple PendulumsAt what position in the cycle of a swinging
pendulum is the potential energy of the pendulum at a maximum
Simple Harmonic Motion Calculations
2L
Tg
2m
Tk
For a simple pendulum in simple harmonic motion
For a mass-spring system in simple harmonic motion
WavesMedium ndash a physical environment through
which a disturbance can travel
Mechanical wave ndash a wave that requires a medium to travel through
Examples Non-examples
Transverse Waves
Wave motion is perpendicular to equilibrium
Transverse Waves
Transerve Waves
Longitudinal Waves
Wave motion is parallel to equilibrium
Wave PropertiesPulse wave
A wave that is just one interference ndash no repetition
Reflection
Constructive and Destructive Interference Constructive interference
A superposition of two or more waves in which individual displacements on the same side of the equilibrium position are added together to form the resultant wave
Constructive and Destructive Interference Destructive interference
A superposition of two or more waves in which individual displacements on opposite sides of the equilibrium position are added together to form the resultant wave
Speed of a Wavespeed of a wave = (frequency) (wavelength)
v = f λ
1 A piano emits frequencies that range from a low of about 28 Hz to a high of about 4200 Hz Find the range of wavelengths in air attained by this instrument when the speed of sound in air is 340 ms
2 The red light emitted by a He-Ne laser has a wavelength of 633 nm in air and travels at the speed of light (300 x 108 ms) Find the frequency of the laser light
De Broglie WavesLouis de Broglie suggested that all matter has wavelike characteristics
where h is Planckrsquos constant equal to 663 x 10-
34 Js
This wavelength is too small to notice interference for large objects This idea becomes important when looking all things at the microscopic level
h h
p mv
De Broglie WavesWhat is the wavelength of an electron (mass = 911 x 10macr31 kg) traveling at 531 x 106 ms
Hookersquos LawIf a mass of 055 kg attached to a vertical spring stretches the spring 20 cm from its original equilibrium what is the spring constant
Simple Harmonic MotionVibration about an equilibrium position in
which a restoring force is proportional to the displacement from equilibrium
Simple PendulumsAmplitude
Length
Period
Frequency
Simple Pendulums
Simple PendulumsAt what position in the cycle of a swinging
pendulum is the potential energy of the pendulum at a maximum
Simple Harmonic Motion Calculations
2L
Tg
2m
Tk
For a simple pendulum in simple harmonic motion
For a mass-spring system in simple harmonic motion
WavesMedium ndash a physical environment through
which a disturbance can travel
Mechanical wave ndash a wave that requires a medium to travel through
Examples Non-examples
Transverse Waves
Wave motion is perpendicular to equilibrium
Transverse Waves
Transerve Waves
Longitudinal Waves
Wave motion is parallel to equilibrium
Wave PropertiesPulse wave
A wave that is just one interference ndash no repetition
Reflection
Constructive and Destructive Interference Constructive interference
A superposition of two or more waves in which individual displacements on the same side of the equilibrium position are added together to form the resultant wave
Constructive and Destructive Interference Destructive interference
A superposition of two or more waves in which individual displacements on opposite sides of the equilibrium position are added together to form the resultant wave
Speed of a Wavespeed of a wave = (frequency) (wavelength)
v = f λ
1 A piano emits frequencies that range from a low of about 28 Hz to a high of about 4200 Hz Find the range of wavelengths in air attained by this instrument when the speed of sound in air is 340 ms
2 The red light emitted by a He-Ne laser has a wavelength of 633 nm in air and travels at the speed of light (300 x 108 ms) Find the frequency of the laser light
De Broglie WavesLouis de Broglie suggested that all matter has wavelike characteristics
where h is Planckrsquos constant equal to 663 x 10-
34 Js
This wavelength is too small to notice interference for large objects This idea becomes important when looking all things at the microscopic level
h h
p mv
De Broglie WavesWhat is the wavelength of an electron (mass = 911 x 10macr31 kg) traveling at 531 x 106 ms
Simple Harmonic MotionVibration about an equilibrium position in
which a restoring force is proportional to the displacement from equilibrium
Simple PendulumsAmplitude
Length
Period
Frequency
Simple Pendulums
Simple PendulumsAt what position in the cycle of a swinging
pendulum is the potential energy of the pendulum at a maximum
Simple Harmonic Motion Calculations
2L
Tg
2m
Tk
For a simple pendulum in simple harmonic motion
For a mass-spring system in simple harmonic motion
WavesMedium ndash a physical environment through
which a disturbance can travel
Mechanical wave ndash a wave that requires a medium to travel through
Examples Non-examples
Transverse Waves
Wave motion is perpendicular to equilibrium
Transverse Waves
Transerve Waves
Longitudinal Waves
Wave motion is parallel to equilibrium
Wave PropertiesPulse wave
A wave that is just one interference ndash no repetition
Reflection
Constructive and Destructive Interference Constructive interference
A superposition of two or more waves in which individual displacements on the same side of the equilibrium position are added together to form the resultant wave
Constructive and Destructive Interference Destructive interference
A superposition of two or more waves in which individual displacements on opposite sides of the equilibrium position are added together to form the resultant wave
Speed of a Wavespeed of a wave = (frequency) (wavelength)
v = f λ
1 A piano emits frequencies that range from a low of about 28 Hz to a high of about 4200 Hz Find the range of wavelengths in air attained by this instrument when the speed of sound in air is 340 ms
2 The red light emitted by a He-Ne laser has a wavelength of 633 nm in air and travels at the speed of light (300 x 108 ms) Find the frequency of the laser light
De Broglie WavesLouis de Broglie suggested that all matter has wavelike characteristics
where h is Planckrsquos constant equal to 663 x 10-
34 Js
This wavelength is too small to notice interference for large objects This idea becomes important when looking all things at the microscopic level
h h
p mv
De Broglie WavesWhat is the wavelength of an electron (mass = 911 x 10macr31 kg) traveling at 531 x 106 ms
Simple PendulumsAmplitude
Length
Period
Frequency
Simple Pendulums
Simple PendulumsAt what position in the cycle of a swinging
pendulum is the potential energy of the pendulum at a maximum
Simple Harmonic Motion Calculations
2L
Tg
2m
Tk
For a simple pendulum in simple harmonic motion
For a mass-spring system in simple harmonic motion
WavesMedium ndash a physical environment through
which a disturbance can travel
Mechanical wave ndash a wave that requires a medium to travel through
Examples Non-examples
Transverse Waves
Wave motion is perpendicular to equilibrium
Transverse Waves
Transerve Waves
Longitudinal Waves
Wave motion is parallel to equilibrium
Wave PropertiesPulse wave
A wave that is just one interference ndash no repetition
Reflection
Constructive and Destructive Interference Constructive interference
A superposition of two or more waves in which individual displacements on the same side of the equilibrium position are added together to form the resultant wave
Constructive and Destructive Interference Destructive interference
A superposition of two or more waves in which individual displacements on opposite sides of the equilibrium position are added together to form the resultant wave
Speed of a Wavespeed of a wave = (frequency) (wavelength)
v = f λ
1 A piano emits frequencies that range from a low of about 28 Hz to a high of about 4200 Hz Find the range of wavelengths in air attained by this instrument when the speed of sound in air is 340 ms
2 The red light emitted by a He-Ne laser has a wavelength of 633 nm in air and travels at the speed of light (300 x 108 ms) Find the frequency of the laser light
De Broglie WavesLouis de Broglie suggested that all matter has wavelike characteristics
where h is Planckrsquos constant equal to 663 x 10-
34 Js
This wavelength is too small to notice interference for large objects This idea becomes important when looking all things at the microscopic level
h h
p mv
De Broglie WavesWhat is the wavelength of an electron (mass = 911 x 10macr31 kg) traveling at 531 x 106 ms
Simple Pendulums
Simple PendulumsAt what position in the cycle of a swinging
pendulum is the potential energy of the pendulum at a maximum
Simple Harmonic Motion Calculations
2L
Tg
2m
Tk
For a simple pendulum in simple harmonic motion
For a mass-spring system in simple harmonic motion
WavesMedium ndash a physical environment through
which a disturbance can travel
Mechanical wave ndash a wave that requires a medium to travel through
Examples Non-examples
Transverse Waves
Wave motion is perpendicular to equilibrium
Transverse Waves
Transerve Waves
Longitudinal Waves
Wave motion is parallel to equilibrium
Wave PropertiesPulse wave
A wave that is just one interference ndash no repetition
Reflection
Constructive and Destructive Interference Constructive interference
A superposition of two or more waves in which individual displacements on the same side of the equilibrium position are added together to form the resultant wave
Constructive and Destructive Interference Destructive interference
A superposition of two or more waves in which individual displacements on opposite sides of the equilibrium position are added together to form the resultant wave
Speed of a Wavespeed of a wave = (frequency) (wavelength)
v = f λ
1 A piano emits frequencies that range from a low of about 28 Hz to a high of about 4200 Hz Find the range of wavelengths in air attained by this instrument when the speed of sound in air is 340 ms
2 The red light emitted by a He-Ne laser has a wavelength of 633 nm in air and travels at the speed of light (300 x 108 ms) Find the frequency of the laser light
De Broglie WavesLouis de Broglie suggested that all matter has wavelike characteristics
where h is Planckrsquos constant equal to 663 x 10-
34 Js
This wavelength is too small to notice interference for large objects This idea becomes important when looking all things at the microscopic level
h h
p mv
De Broglie WavesWhat is the wavelength of an electron (mass = 911 x 10macr31 kg) traveling at 531 x 106 ms
Simple PendulumsAt what position in the cycle of a swinging
pendulum is the potential energy of the pendulum at a maximum
Simple Harmonic Motion Calculations
2L
Tg
2m
Tk
For a simple pendulum in simple harmonic motion
For a mass-spring system in simple harmonic motion
WavesMedium ndash a physical environment through
which a disturbance can travel
Mechanical wave ndash a wave that requires a medium to travel through
Examples Non-examples
Transverse Waves
Wave motion is perpendicular to equilibrium
Transverse Waves
Transerve Waves
Longitudinal Waves
Wave motion is parallel to equilibrium
Wave PropertiesPulse wave
A wave that is just one interference ndash no repetition
Reflection
Constructive and Destructive Interference Constructive interference
A superposition of two or more waves in which individual displacements on the same side of the equilibrium position are added together to form the resultant wave
Constructive and Destructive Interference Destructive interference
A superposition of two or more waves in which individual displacements on opposite sides of the equilibrium position are added together to form the resultant wave
Speed of a Wavespeed of a wave = (frequency) (wavelength)
v = f λ
1 A piano emits frequencies that range from a low of about 28 Hz to a high of about 4200 Hz Find the range of wavelengths in air attained by this instrument when the speed of sound in air is 340 ms
2 The red light emitted by a He-Ne laser has a wavelength of 633 nm in air and travels at the speed of light (300 x 108 ms) Find the frequency of the laser light
De Broglie WavesLouis de Broglie suggested that all matter has wavelike characteristics
where h is Planckrsquos constant equal to 663 x 10-
34 Js
This wavelength is too small to notice interference for large objects This idea becomes important when looking all things at the microscopic level
h h
p mv
De Broglie WavesWhat is the wavelength of an electron (mass = 911 x 10macr31 kg) traveling at 531 x 106 ms
Simple Harmonic Motion Calculations
2L
Tg
2m
Tk
For a simple pendulum in simple harmonic motion
For a mass-spring system in simple harmonic motion
WavesMedium ndash a physical environment through
which a disturbance can travel
Mechanical wave ndash a wave that requires a medium to travel through
Examples Non-examples
Transverse Waves
Wave motion is perpendicular to equilibrium
Transverse Waves
Transerve Waves
Longitudinal Waves
Wave motion is parallel to equilibrium
Wave PropertiesPulse wave
A wave that is just one interference ndash no repetition
Reflection
Constructive and Destructive Interference Constructive interference
A superposition of two or more waves in which individual displacements on the same side of the equilibrium position are added together to form the resultant wave
Constructive and Destructive Interference Destructive interference
A superposition of two or more waves in which individual displacements on opposite sides of the equilibrium position are added together to form the resultant wave
Speed of a Wavespeed of a wave = (frequency) (wavelength)
v = f λ
1 A piano emits frequencies that range from a low of about 28 Hz to a high of about 4200 Hz Find the range of wavelengths in air attained by this instrument when the speed of sound in air is 340 ms
2 The red light emitted by a He-Ne laser has a wavelength of 633 nm in air and travels at the speed of light (300 x 108 ms) Find the frequency of the laser light
De Broglie WavesLouis de Broglie suggested that all matter has wavelike characteristics
where h is Planckrsquos constant equal to 663 x 10-
34 Js
This wavelength is too small to notice interference for large objects This idea becomes important when looking all things at the microscopic level
h h
p mv
De Broglie WavesWhat is the wavelength of an electron (mass = 911 x 10macr31 kg) traveling at 531 x 106 ms
WavesMedium ndash a physical environment through
which a disturbance can travel
Mechanical wave ndash a wave that requires a medium to travel through
Examples Non-examples
Transverse Waves
Wave motion is perpendicular to equilibrium
Transverse Waves
Transerve Waves
Longitudinal Waves
Wave motion is parallel to equilibrium
Wave PropertiesPulse wave
A wave that is just one interference ndash no repetition
Reflection
Constructive and Destructive Interference Constructive interference
A superposition of two or more waves in which individual displacements on the same side of the equilibrium position are added together to form the resultant wave
Constructive and Destructive Interference Destructive interference
A superposition of two or more waves in which individual displacements on opposite sides of the equilibrium position are added together to form the resultant wave
Speed of a Wavespeed of a wave = (frequency) (wavelength)
v = f λ
1 A piano emits frequencies that range from a low of about 28 Hz to a high of about 4200 Hz Find the range of wavelengths in air attained by this instrument when the speed of sound in air is 340 ms
2 The red light emitted by a He-Ne laser has a wavelength of 633 nm in air and travels at the speed of light (300 x 108 ms) Find the frequency of the laser light
De Broglie WavesLouis de Broglie suggested that all matter has wavelike characteristics
where h is Planckrsquos constant equal to 663 x 10-
34 Js
This wavelength is too small to notice interference for large objects This idea becomes important when looking all things at the microscopic level
h h
p mv
De Broglie WavesWhat is the wavelength of an electron (mass = 911 x 10macr31 kg) traveling at 531 x 106 ms
Transverse Waves
Wave motion is perpendicular to equilibrium
Transverse Waves
Transerve Waves
Longitudinal Waves
Wave motion is parallel to equilibrium
Wave PropertiesPulse wave
A wave that is just one interference ndash no repetition
Reflection
Constructive and Destructive Interference Constructive interference
A superposition of two or more waves in which individual displacements on the same side of the equilibrium position are added together to form the resultant wave
Constructive and Destructive Interference Destructive interference
A superposition of two or more waves in which individual displacements on opposite sides of the equilibrium position are added together to form the resultant wave
Speed of a Wavespeed of a wave = (frequency) (wavelength)
v = f λ
1 A piano emits frequencies that range from a low of about 28 Hz to a high of about 4200 Hz Find the range of wavelengths in air attained by this instrument when the speed of sound in air is 340 ms
2 The red light emitted by a He-Ne laser has a wavelength of 633 nm in air and travels at the speed of light (300 x 108 ms) Find the frequency of the laser light
De Broglie WavesLouis de Broglie suggested that all matter has wavelike characteristics
where h is Planckrsquos constant equal to 663 x 10-
34 Js
This wavelength is too small to notice interference for large objects This idea becomes important when looking all things at the microscopic level
h h
p mv
De Broglie WavesWhat is the wavelength of an electron (mass = 911 x 10macr31 kg) traveling at 531 x 106 ms
Transverse Waves
Transerve Waves
Longitudinal Waves
Wave motion is parallel to equilibrium
Wave PropertiesPulse wave
A wave that is just one interference ndash no repetition
Reflection
Constructive and Destructive Interference Constructive interference
A superposition of two or more waves in which individual displacements on the same side of the equilibrium position are added together to form the resultant wave
Constructive and Destructive Interference Destructive interference
A superposition of two or more waves in which individual displacements on opposite sides of the equilibrium position are added together to form the resultant wave
Speed of a Wavespeed of a wave = (frequency) (wavelength)
v = f λ
1 A piano emits frequencies that range from a low of about 28 Hz to a high of about 4200 Hz Find the range of wavelengths in air attained by this instrument when the speed of sound in air is 340 ms
2 The red light emitted by a He-Ne laser has a wavelength of 633 nm in air and travels at the speed of light (300 x 108 ms) Find the frequency of the laser light
De Broglie WavesLouis de Broglie suggested that all matter has wavelike characteristics
where h is Planckrsquos constant equal to 663 x 10-
34 Js
This wavelength is too small to notice interference for large objects This idea becomes important when looking all things at the microscopic level
h h
p mv
De Broglie WavesWhat is the wavelength of an electron (mass = 911 x 10macr31 kg) traveling at 531 x 106 ms
Transerve Waves
Longitudinal Waves
Wave motion is parallel to equilibrium
Wave PropertiesPulse wave
A wave that is just one interference ndash no repetition
Reflection
Constructive and Destructive Interference Constructive interference
A superposition of two or more waves in which individual displacements on the same side of the equilibrium position are added together to form the resultant wave
Constructive and Destructive Interference Destructive interference
A superposition of two or more waves in which individual displacements on opposite sides of the equilibrium position are added together to form the resultant wave
Speed of a Wavespeed of a wave = (frequency) (wavelength)
v = f λ
1 A piano emits frequencies that range from a low of about 28 Hz to a high of about 4200 Hz Find the range of wavelengths in air attained by this instrument when the speed of sound in air is 340 ms
2 The red light emitted by a He-Ne laser has a wavelength of 633 nm in air and travels at the speed of light (300 x 108 ms) Find the frequency of the laser light
De Broglie WavesLouis de Broglie suggested that all matter has wavelike characteristics
where h is Planckrsquos constant equal to 663 x 10-
34 Js
This wavelength is too small to notice interference for large objects This idea becomes important when looking all things at the microscopic level
h h
p mv
De Broglie WavesWhat is the wavelength of an electron (mass = 911 x 10macr31 kg) traveling at 531 x 106 ms
Longitudinal Waves
Wave motion is parallel to equilibrium
Wave PropertiesPulse wave
A wave that is just one interference ndash no repetition
Reflection
Constructive and Destructive Interference Constructive interference
A superposition of two or more waves in which individual displacements on the same side of the equilibrium position are added together to form the resultant wave
Constructive and Destructive Interference Destructive interference
A superposition of two or more waves in which individual displacements on opposite sides of the equilibrium position are added together to form the resultant wave
Speed of a Wavespeed of a wave = (frequency) (wavelength)
v = f λ
1 A piano emits frequencies that range from a low of about 28 Hz to a high of about 4200 Hz Find the range of wavelengths in air attained by this instrument when the speed of sound in air is 340 ms
2 The red light emitted by a He-Ne laser has a wavelength of 633 nm in air and travels at the speed of light (300 x 108 ms) Find the frequency of the laser light
De Broglie WavesLouis de Broglie suggested that all matter has wavelike characteristics
where h is Planckrsquos constant equal to 663 x 10-
34 Js
This wavelength is too small to notice interference for large objects This idea becomes important when looking all things at the microscopic level
h h
p mv
De Broglie WavesWhat is the wavelength of an electron (mass = 911 x 10macr31 kg) traveling at 531 x 106 ms
Wave PropertiesPulse wave
A wave that is just one interference ndash no repetition
Reflection
Constructive and Destructive Interference Constructive interference
A superposition of two or more waves in which individual displacements on the same side of the equilibrium position are added together to form the resultant wave
Constructive and Destructive Interference Destructive interference
A superposition of two or more waves in which individual displacements on opposite sides of the equilibrium position are added together to form the resultant wave
Speed of a Wavespeed of a wave = (frequency) (wavelength)
v = f λ
1 A piano emits frequencies that range from a low of about 28 Hz to a high of about 4200 Hz Find the range of wavelengths in air attained by this instrument when the speed of sound in air is 340 ms
2 The red light emitted by a He-Ne laser has a wavelength of 633 nm in air and travels at the speed of light (300 x 108 ms) Find the frequency of the laser light
De Broglie WavesLouis de Broglie suggested that all matter has wavelike characteristics
where h is Planckrsquos constant equal to 663 x 10-
34 Js
This wavelength is too small to notice interference for large objects This idea becomes important when looking all things at the microscopic level
h h
p mv
De Broglie WavesWhat is the wavelength of an electron (mass = 911 x 10macr31 kg) traveling at 531 x 106 ms
Constructive and Destructive Interference Constructive interference
A superposition of two or more waves in which individual displacements on the same side of the equilibrium position are added together to form the resultant wave
Constructive and Destructive Interference Destructive interference
A superposition of two or more waves in which individual displacements on opposite sides of the equilibrium position are added together to form the resultant wave
Speed of a Wavespeed of a wave = (frequency) (wavelength)
v = f λ
1 A piano emits frequencies that range from a low of about 28 Hz to a high of about 4200 Hz Find the range of wavelengths in air attained by this instrument when the speed of sound in air is 340 ms
2 The red light emitted by a He-Ne laser has a wavelength of 633 nm in air and travels at the speed of light (300 x 108 ms) Find the frequency of the laser light
De Broglie WavesLouis de Broglie suggested that all matter has wavelike characteristics
where h is Planckrsquos constant equal to 663 x 10-
34 Js
This wavelength is too small to notice interference for large objects This idea becomes important when looking all things at the microscopic level
h h
p mv
De Broglie WavesWhat is the wavelength of an electron (mass = 911 x 10macr31 kg) traveling at 531 x 106 ms
Constructive and Destructive Interference Destructive interference
A superposition of two or more waves in which individual displacements on opposite sides of the equilibrium position are added together to form the resultant wave
Speed of a Wavespeed of a wave = (frequency) (wavelength)
v = f λ
1 A piano emits frequencies that range from a low of about 28 Hz to a high of about 4200 Hz Find the range of wavelengths in air attained by this instrument when the speed of sound in air is 340 ms
2 The red light emitted by a He-Ne laser has a wavelength of 633 nm in air and travels at the speed of light (300 x 108 ms) Find the frequency of the laser light
De Broglie WavesLouis de Broglie suggested that all matter has wavelike characteristics
where h is Planckrsquos constant equal to 663 x 10-
34 Js
This wavelength is too small to notice interference for large objects This idea becomes important when looking all things at the microscopic level
h h
p mv
De Broglie WavesWhat is the wavelength of an electron (mass = 911 x 10macr31 kg) traveling at 531 x 106 ms
Speed of a Wavespeed of a wave = (frequency) (wavelength)
v = f λ
1 A piano emits frequencies that range from a low of about 28 Hz to a high of about 4200 Hz Find the range of wavelengths in air attained by this instrument when the speed of sound in air is 340 ms
2 The red light emitted by a He-Ne laser has a wavelength of 633 nm in air and travels at the speed of light (300 x 108 ms) Find the frequency of the laser light
De Broglie WavesLouis de Broglie suggested that all matter has wavelike characteristics
where h is Planckrsquos constant equal to 663 x 10-
34 Js
This wavelength is too small to notice interference for large objects This idea becomes important when looking all things at the microscopic level
h h
p mv
De Broglie WavesWhat is the wavelength of an electron (mass = 911 x 10macr31 kg) traveling at 531 x 106 ms
De Broglie WavesLouis de Broglie suggested that all matter has wavelike characteristics
where h is Planckrsquos constant equal to 663 x 10-
34 Js
This wavelength is too small to notice interference for large objects This idea becomes important when looking all things at the microscopic level
h h
p mv
De Broglie WavesWhat is the wavelength of an electron (mass = 911 x 10macr31 kg) traveling at 531 x 106 ms
De Broglie WavesWhat is the wavelength of an electron (mass = 911 x 10macr31 kg) traveling at 531 x 106 ms
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