Chapter 12 Vibrations & Waves Physics

Vibrations & Waves  Simple Harmonic Motion Hooke’s Law Hooke’s Law The Force of a Spring is Always Opposite of the Direction of the Mass’s Displacement from EquilibriumThe Force of a Spring is Always Opposite of the Direction of the Mass’s Displacement from Equilibrium

Vibrations & Waves  Simple Harmonic Motion Hooke’s Law Hooke’s Law

Vibrations & Waves  Simple Harmonic Motion The Pendulum The Pendulum The Force of the “x” Component of the Weight Always Points Toward the Equilibrium positionThe Force of the “x” Component of the Weight Always Points Toward the Equilibrium position

Vibrations & Waves  Simple Harmonic Motion Conservation of Energy Conservation of Energy PE  KE  PE …PE  KE  PE …

Vibrations & Waves  Simple Harmonic Motion  Amplitude (A)  Magnitude of the Oscillation  Positive or Negative

Vibrations & Waves  Simple Harmonic Motion  Period (T)  Time Required for One Complete Cycle  Seconds/Cycle  Units = Second

Vibrations & Waves  Simple Harmonic Motion  Frequency (f)  Number of Cycles/Second  Units: Hertz (Hz)

Vibrations & Waves  Simple Harmonic Motion  Frequency (f)  Period (T)

Vibrations & Waves  Simple Harmonic Motion  Period of a Pendulum

Vibrations & Waves  Simple Harmonic Motion  Period of a Mass-Spring

Vibrations & Waves  Simple Harmonic Motion  Wave Relationship

Vibrations & Waves  Waves Traveling Disturbance Traveling Disturbance Carry Energy Carry Energy

Vibrations & Waves  Mechanical Waves Require a Medium Require a Medium Examples Examples Water WavesWater Waves Waves in a …Waves in a … Spring Spring Rope Rope Sound WavesSound Waves

Vibrations & Waves  Wave Pulse Single Input Produces a Single Wave Single Input Produces a Single Wave  Continuous Wave A Repeated Sequence of Wave Pulses A Repeated Sequence of Wave Pulses Periodic Wave Periodic Wave

Vibrations & Waves  Transverse Wave Perpendicular to Direction of Travel Perpendicular to Direction of Travel ex. ex. Radio WavesRadio Waves LightLight MicrowavesMicrowaves (all are frequencies of electromagnetic radiation)(all are frequencies of electromagnetic radiation)

Vibrations & Waves  Longitudinal Wave Parallel to Direction of Travel Parallel to Direction of Travel ex. ex. SoundSound FluidsFluids

Vibrations & Waves  Wave Terminology Cycle Cycle Crest Crest Trough Trough Wavelength ( ) Wavelength ( ) Amplitude (A) Frequency (f) Period (T) Velocity (v)

Vibrations & Waves  Cycle Wave Pattern Beginning at Undisturbed Position and Ending at Return to Undisturbed Position Wave Pattern Beginning at Undisturbed Position and Ending at Return to Undisturbed Position

Vibrations & Waves  Crest Maximum Distance from Undisturbed Position to Wave Position in a Positive Direction (High Point of the Wave) Maximum Distance from Undisturbed Position to Wave Position in a Positive Direction (High Point of the Wave)

Vibrations & Waves  Trough Maximum Distance from Undisturbed Position to Wave Position in a Negative Direction (Low Point of the Wave) Maximum Distance from Undisturbed Position to Wave Position in a Negative Direction (Low Point of the Wave)

Vibrations & Waves  Wavelength ( ) Distance Between Any Two Successive Equivalent Points On A Wave Distance Between Any Two Successive Equivalent Points On A Wave Measured in Meters (m) Measured in Meters (m)

Vibrations & Waves  Amplitude (A) Maximum Distance from Undisturbed Position to Peak of Crest or Bottom of Trough Maximum Distance from Undisturbed Position to Peak of Crest or Bottom of Trough

Vibrations & Waves  Frequency (f) Number of cycles/second Number of cycles/second Measured in Hertz (Hz) Measured in Hertz (Hz) 1cycle/sec = 1 Hz 1cycle/sec = 1 Hz

Vibrations & Waves  Period (T) Number of Seconds/Cycle Number of Seconds/Cycle Measured in Seconds (s) Measured in Seconds (s) Time Required for One Cycle Time Required for One Cycle

Vibrations & Waves  Frequency-Period Relationship Period = Seconds/Cycle Period = Seconds/Cycle Frequency = Cycles/Second Frequency = Cycles/Second So… So…

Vibrations & Waves  Wave Speed (v) Velocity of traveling wavelength Velocity of traveling wavelength Wavelength is in Meters (m) Wavelength is in Meters (m) Frequency is Cycles/Second Frequency is Cycles/Second Velocity is meters/second (m/s) Velocity is meters/second (m/s)

Vibrations & Waves  Problem The Sears Tower sways back and forth in the wind with a frequency of about 0.10Hz. How much time does it take for each back and forth motion? The Sears Tower sways back and forth in the wind with a frequency of about 0.10Hz. How much time does it take for each back and forth motion?

Vibrations & Waves  Solution f = 0.10Hz f = 0.10Hz

Vibrations & Waves  Problem Water waves in a shallow dish are 6.0cm long. At one point, the water oscillates up and down at a rate of 4.8 oscillations per second. What is the velocity of the waves? Water waves in a shallow dish are 6.0cm long. At one point, the water oscillates up and down at a rate of 4.8 oscillations per second. What is the velocity of the waves?

Vibrations & Waves  Solution  = 6.0cm  = 6.0cm f = 4.8Hz f = 4.8Hz

Vibrations & Waves  Problem Water waves in a shallow dish are 6.0cm long. At one point, the water oscillates up and down at a rate of 4.8 oscillations per second. What is the period of the waves? Water waves in a shallow dish are 6.0cm long. At one point, the water oscillates up and down at a rate of 4.8 oscillations per second. What is the period of the waves?

Vibrations & Waves  Solution  = 6.0cm  = 6.0cm f = 4.8Hz f = 4.8Hz

Vibrations & Waves  Problem The frequency of yellow light is 5.0x10 14 Hz. What is the wavelength of yellow light? (c=3x10 8 m/s) The frequency of yellow light is 5.0x10 14 Hz. What is the wavelength of yellow light? (c=3x10 8 m/s)

Vibrations & Waves  Solution f = 5.0x10 14 Hz f = 5.0x10 14 Hz c = 3x10 8 m/s c = 3x10 8 m/s

Vibrations & Waves  Problem A sonar signal with a frequency of 1.00x10 6 Hz has a wavelength of 1.50mm in water. What is the speed of the signal in water? A sonar signal with a frequency of 1.00x10 6 Hz has a wavelength of 1.50mm in water. What is the speed of the signal in water?

Vibrations & Waves  Solution f = 1.00x10 6 Hz f = 1.00x10 6 Hz = 1.50x10 -3 m = 1.50x10 -3 m

Vibrations & Waves  Problem A sonar signal with a frequency of 1.00x10 6 Hz has a wavelength of 1.50mm in water. What is the period of the signal in water? A sonar signal with a frequency of 1.00x10 6 Hz has a wavelength of 1.50mm in water. What is the period of the signal in water?

Vibrations & Waves  Solution f = 1.00x10 6 Hz f = 1.00x10 6 Hz = 1.50x10 -3 m = 1.50x10 -3 m v = 1.50x10 3 m/s v = 1.50x10 3 m/s

Vibrations & Waves  Problem A sonar signal with a frequency of 1.00x10 6 Hz has a wavelength of 1.50mm in water. What is the period of the signal in air? A sonar signal with a frequency of 1.00x10 6 Hz has a wavelength of 1.50mm in water. What is the period of the signal in air?

Vibrations & Waves  Solution f = 1.00x10 6 Hz f = 1.00x10 6 Hz = 1.50x10 -3 m = 1.50x10 -3 m v = 1.50x10 3 m/s v = 1.50x10 3 m/s T = 1.00x10 -6 s T = 1.00x10 -6 s The period and frequency will not change in air The period and frequency will not change in air

Vibrations & Waves  Problem The speed of sound in water is 1498m/s. A sonar signal is sent straight down from a ship at a point just below the water’s surface, and 1.80s later the reflected signal is detected at the ship. How deep is the water beneath the ship? The speed of sound in water is 1498m/s. A sonar signal is sent straight down from a ship at a point just below the water’s surface, and 1.80s later the reflected signal is detected at the ship. How deep is the water beneath the ship?

Vibrations & Waves  Solution  t = 1.8s  t = 1.8s v = 1498m/s v = 1498m/s

Vibrations & Waves  Problem Erin and Lauren are resting on an offshore raft after a swim. They estimate that 3.0m separates a trough and an adjacent crest of the surface waves. They count 14 crests that pass by the raft in 20.0s. What is the velocity of the waves? Erin and Lauren are resting on an offshore raft after a swim. They estimate that 3.0m separates a trough and an adjacent crest of the surface waves. They count 14 crests that pass by the raft in 20.0s. What is the velocity of the waves?

Vibrations & Waves  Solution  t = 20.0s  t = 20.0s = 6.0m = 6.0m waves = 14 waves = 14

Vibrations & Waves  Homework Pages 469 – 471 Pages 469 – 471 ProblemsProblems 9 (580N/m) 9 (580N/m) 20 (22.4m) 20 (22.4m) 21 (a, 2.0s b, 9.812m/s 2 c, 9.798m/s 2 ) 21 (a, 2.0s b, 9.812m/s 2 c, 9.798m/s 2 ) 36 (0.0333m) 36 (0.0333m)

Vibrations & Waves  Wave Behavior Varies With Medium Varies With Medium Sound in AirSound in Air Sound in HeSound in He VideoVideoVideo

Vibrations & Waves  The Principle of Linear Superposition “When Two or More Waves are Present Simultaneously at the Same Place, the Resultant Disturbance is the Sum of the Disturbances from the Individual Waves” “When Two or More Waves are Present Simultaneously at the Same Place, the Resultant Disturbance is the Sum of the Disturbances from the Individual Waves”

Vibrations & Waves  The Principle of Linear Superposition The Merging of Two or More Waves The Merging of Two or More Waves Coherent SourcesCoherent Sources The Resultant Wave is the Sum of the Combined Waves The Resultant Wave is the Sum of the Combined Waves AmplitudeAmplitude DirectionDirection

Vibrations & Waves  Constructive and Destructive Interference

Vibrations & Waves  Constructive and Destructive Interference In Phase: Constructive Interference In Phase: Constructive Interference Condensations and Rarefactions of Two or More Waves Meet (C-C & R-R)Condensations and Rarefactions of Two or More Waves Meet (C-C & R-R)

Vibrations & Waves  Constructive and Destructive Interference In Phase: Constructive Interference In Phase: Constructive Interference Amplitude Equals the Sum of Amplitude “A” and Amplitude “B”Amplitude Equals the Sum of Amplitude “A” and Amplitude “B”

Vibrations & Waves  Constructive and Destructive Interference Out of Phase (Exactly): Destructive Interference Out of Phase (Exactly): Destructive Interference Condensations and Rarefactions of Two or More Waves Meet (C-R & C-R)Condensations and Rarefactions of Two or More Waves Meet (C-R & C-R)

Vibrations & Waves  Constructive and Destructive Interference Out of Phase (Exactly): Destructive Interference Out of Phase (Exactly): Destructive Interference Amplitude Equals the Sum of Amplitude “A” and Amplitude “B”Amplitude Equals the Sum of Amplitude “A” and Amplitude “B” Mutual CancellationMutual Cancellation When Referring to Sound Waves: No SoundWhen Referring to Sound Waves: No Sound

Vibrations & Waves  Constructive and Destructive Interference Conservation of Energy Conservation of Energy Energy is Neither Created Nor DestroyedEnergy is Neither Created Nor Destroyed Interference = Energy RedistributionInterference = Energy Redistribution

Vibrations & Waves  Problem The drawing shows a string on which two rectangular pulses are traveling at a constant speed of 1cm/s at time = 0. Using the principal of linear superposition, draw the shape of the string at t = 1s, 2s, 3s, 4s, and 5s. The drawing shows a string on which two rectangular pulses are traveling at a constant speed of 1cm/s at time = 0. Using the principal of linear superposition, draw the shape of the string at t = 1s, 2s, 3s, 4s, and 5s Distance, cm

Vibrations & Waves  Solution t = 0s t = 0s Distance, cm

Vibrations & Waves  Solution t = 1s t = 1s Distance, cm

Vibrations & Waves  Solution t = 2s t = 2s Distance, cm

Vibrations & Waves  Solution t = 3s t = 3s Distance, cm

Vibrations & Waves  Solution t = 4s t = 4s Distance, cm

Vibrations & Waves  Solution t = 5s t = 5s Distance, cm

Vibrations & Waves  Reflection of Waves Waves will be reflected either erect or inverted Waves will be reflected either erect or inverted Erect Erect Wave is orientated the same as the originalWave is orientated the same as the original Inverted Inverted Wave is orientated opposite of the originalWave is orientated opposite of the original

Vibrations & Waves  Reflection of Waves Erect Erect Reflected off a medium that is less dense than wave source medium (Free Boundary)Reflected off a medium that is less dense than wave source medium (Free Boundary) Inverted Inverted Reflected off a medium that is more dense than wave source medium (Fixed Boundary)Reflected off a medium that is more dense than wave source medium (Fixed Boundary)

Vibrations & Waves  Transverse Standing Waves Not Really “Standing” at All Not Really “Standing” at All Reflection of a Wave Producing ResonanceReflection of a Wave Producing Resonance

Vibrations & Waves  Transverse Standing Waves Certain Resonance Frequencies Produce Different Standing Waves Certain Resonance Frequencies Produce Different Standing Waves

Vibrations & Waves  Transverse Standing Waves Node Node Destructive InterferenceDestructive Interference Antinode Antinode Constructive InterferenceConstructive Interference

Vibrations & Waves  Homework Pages Pages ProblemsProblems (446m) 50 (446m) 58 (9:48am) 58 (9:48am)