Vibrations & Waves
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Transcript of Vibrations & Waves
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Vibrations & Waves
Chapter 25 - This will be phun!
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2 Types of WavesMechanical Wave:
Requires a mechanical mediumSound, water, air, springs, or ropes are examples.
Electromagnetic Waves (EM):Does not require a medium for motion to occurLight, Radio, and X-rays are examples.
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“Making Waves”
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Transverse WavesCauses the particles of the medium to vibrate perpendicularly to the direction of motion of the wave.Piano and guitar strings are examples
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Longitudinal WavesWhen particles of the medium move parallel to the direction of the waves.Fluids, liquids, gases, or plasma usually transmit only longitudinal waves.
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Longitudinal and Transverse
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Longitudinal vs Transverse Waves
Compression = CrestRarefaction = TroughEnergy Movement:parallel vs perpendicularWavelength: compression + rarefaction
crest + trough
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Surface Waves
They are a mixture of transverse and longitudinal waves. (water & Rayleigh)The particles move both parallel and perpendicular to the direction of the wave.
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Wave Pulse and Traveling WaveWave Pulse:
A single disturbance that travels through a medium.
Traveling Wave:Moving, periodic disturbances in a medium or field.
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PeriodThe shortest time interval during which the motion repeats itself.Abbreviated with the capital letter,TSI Unit: seconds (s)
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FrequencyThe number of complete revolutions per second.Frequency is abbreviated with a fancy ƒ.Frequency is measured in Hertz, Hz.A Hertz is one vibration per second (1/s).
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EquationFrequency and the period of a wave are
related by the following equation.
Frequency and Period are reciprocals of each other.
1T
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Wavelength
The shortest distance between points where the wave pattern repeats itself.The wavelength is abbreviated with the Greek letter, lambda,
A: ?B: ?C: ?D: ?E: ?
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Wavelength
The shortest distance between points where the wave pattern repeats itself.The wavelength is abbreviated with the Greek letter, lambda,
A: 1 WavelengthB: 2X AmplitudeC: NodesD: AmplitudeE: ½ Wavelength
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VocabularyCrests:
The high points of each wave motion.
Troughs:The low points of each wave motion
Amplitude:The maximum displacement from the rest or equilibrium position.
Nodes:Where the wave crosses the equilibrium line.
Antinodes:The bottom of the trough and the top of the crest
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VocabularyCrests:
The high points of each wave motion.
Troughs:The low points of each wave motion
Amplitude:The maximum displacement from the rest or equilibrium position.
Nodes:Where the wave crosses the equilibrium line.
Antinodes:The bottom of the trough and the top of the crest
A&F: Crests (Antinodes)D&I: Troughs (Antinodes)B,E,G,J: Nodes
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To find the velocity of a waveWave velocity (v) is the product of the frequency (f) and wavelength ().To find out how fast a wave moves, you would use this equation…
=or v T
=v
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Amplitude and EnergyIn order to produce a wave with a larger amplitude, more energy is needed.Waves with larger amplitudes transfer more energy.Amplitude does not affect frequency nor velocity.
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Waves Changing MediumsWaves passing from one medium to another have the same frequency.The wavelength change depends on the velocity change so that f is constant.
If the velocity increases, the wavelength increases (direct relationship).
v/
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Superposition and InterferencePrinciple of Superposition:
Two or more waves occupying the same space.
Interference:The result from two or more waves occupying the same space.
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Constructive InterferenceOccurs when the wave displacements are in phase (crest meets crest or trough meets trough).The result is a wave with a larger amplitude than the individual waves.
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Destructive InterferenceOccurs when the wave displacements are out of phase (crest meets trough).The result is a wave with a smaller amplitude than the individual waves. Red: wave moving right
Blue: wave moving leftGreen: superposition
(Red + Blue wave)
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Destructive InterferenceIf the pulses have unequal amplitudes, destructive interference is not complete. The pulse of the overlap is the algebraic sum of the two pulses.
Red: wave moving rightBlue: wave moving leftGreen: superposition
(Red + Blue wave)
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Standing Wave
When the nodes and antinodes are stationary, the wave appears to be standing still.If you increase the frequency of a standing wave, you will see more nodes.
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Superposition of Waves
A. Two pulses traveling in opposite directionsB. Two sine waves traveling in the same direction, but at different speedsC. Two sine waves traveling in opposite directions.
http://paws.kettering.edu/~drussell/Demos/superposition/superposition.html
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Nodes and AntinodesNode:
The point in the medium that is completely undisturbed at all times. A node is produced by destructive interference of waves
Antinode:The point of maximum displacement. An antinode is formed from constructive interference.
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Harmonics
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Let’s check for understanding…The number of nodes in the standing wave shown in the diagram
at the right isa. 6b. 7c. 8d. 14
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Let’s check for understanding…The number of nodes in the standing wave shown in the diagram
at the right is
c. 8
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Let’s check for understanding…The number of
antinodes in the standing wave shown in the diagram at the
right isa. 6b. 7c. 8d. 14
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Let’s check for understanding…The number of
antinodes in the standing wave shown in the diagram at the
right is
b. 7
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Let’s check for understanding…In the standing wave shown,
a. What is the amplitude?b. What is its wavelength?
c. How many nodes are there?d. How many antinodes are there?
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Let’s check for understanding…In the standing wave shown,
a. What is the amplitude? 10 cmb. What is its wavelength?
c. How many nodes are there?d. How many antinodes are there?
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Let’s check for understanding…In the standing wave shown,
a. What is the amplitude? 10 cmb. What is its wavelength? 1 mc. How many nodes are there?
d. How many antinodes are there?
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Let’s check for understanding…In the standing wave shown,
a. What is the amplitude? 10 cmb. What is its wavelength? 1 m
c. How many nodes are there? 6d. How many antinodes are there?
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Let’s check for understanding…In the standing wave shown,
a. What is the amplitude? 10 cmb. What is its wavelength? 1 m
c. How many nodes are there? 6d. How many antinodes are there? 5
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Reflection of WavesNormal:
A line that is drawn perpendicular to the barrier (green).
Angle of Incidence:The angle between the incidence ray and the normal.
Angle of Reflection:The angle between the normal and the reflected ray.
>I = >R
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Refraction of WavesRefraction:
The change in the direction of waves at the boundary between two different media.
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Diffraction of WavesDiffraction:
The spreading of waves around the edge of a barrier. Diffraction occurs when waves meet a small obstacle.They can bend around the obstacle, producing waves behind it.
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Problem-Solving
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Springs
Spring Constant
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Spring Constant (stiffness)A spring stretches 18 centimeters when a 56 Newton weight is suspended from it. What is the spring constant?Find: kGivens: d (x) = 18 cm = 0.18 mF = 56 NFormula: k = F dSolution: 310 N/m
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Springs
Potential Energy in a Spring
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Period of a Pendulum
Pendulum
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Using a PendulumA pendulum with a length of 36.9 centimeters has a period of 1.22 seconds. What is the acceleration due to gravity at the pendulum’s location?Find: a (g)Givens: d = 36.9 cm = 0.369 m
T = 1.22 sFormula: g = 42L
T2
Solution: 9.78 m/s2
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Velocity, Wavelength, Frequency and Period Relationships
Wavelength
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WavelengthAn 855 Hertz disturbance moves through an iron rail at a speed of 5130 meters per second. What is the wavelength of the disturbance?Find: Givens: f = 855 Hz
v = 5130 m/sFormula: = v
fSolution: 6.00 m
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Velocity, Wavelength, Frequency and Period Relationships
Period
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PeriodAn 855 Hertz disturbance moves through an iron rail at a speed of 5130 meters per second. What is the period of the disturbance?Find: TGivens: f = 855 HzFormula: T = 1
fSolution: 0.00117 s
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Velocity, Wavelength, Frequency and Period Relationships
Velocity
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VelocityA sound wave has a frequency of 192 Hertz and travels the length of a football field, 91.4 meters, in 0.271 seconds. What is the speed of the wave?Find: vGivens: f = 192 Hz
d = 91.4 mt = 0.271 s
Formula: v = d t
Solution: 337 m/s
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VelocityA sonar signal of frequency 1.00 X 106 Hertz has a wavelength of 1.50 millimeters in water. What is the speed of the signal?Find: vGivens: f = 1.00 X 106 Hz
= 1.50 mm = 0.00150 mFormula: v = fSolution: 1.50 X 103 m/s