Chapter 19 Vibrations and Waves Vibration: A disturbance “wiggle” in time.
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Transcript of Chapter 19 Vibrations and Waves Vibration: A disturbance “wiggle” in time.
![Page 1: Chapter 19 Vibrations and Waves Vibration: A disturbance “wiggle” in time.](https://reader035.fdocuments.us/reader035/viewer/2022062221/56649edf5503460f94befcd3/html5/thumbnails/1.jpg)
Chapter 19Chapter 19
Vibrations and Waves
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• Vibration: A disturbance
“wiggle” in time.
•Wave: A disturbance in
space and time.
![Page 3: Chapter 19 Vibrations and Waves Vibration: A disturbance “wiggle” in time.](https://reader035.fdocuments.us/reader035/viewer/2022062221/56649edf5503460f94befcd3/html5/thumbnails/3.jpg)
Oscillatory Motion
• The to-and-fro vibratory motion, such as that of a pendulum.
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Simple Pendulum
g
L2P
For small displacements, the period of the simple pendulum is related to its length (L) and the acceleration due to gravity (g) by the following:
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Simple Harmonic Motion
• is a type of oscillatory motion in
which the motion repeats itself.
•This motion is caused by a “restoring force” that acts in the opposite direction of the displacement.
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Simple Pendulum
• Under small displacements, the simple pendulum behaves as a harmonic oscillator.
•For a pendulum, the “restoring force” is usually exerted by
GRAVITY
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Amplitude
• The maximum displacement from some equilibrium (mid point) position.
(Applies to both vibrations and waves.)
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Mass-Spring System is Another Example of a Simple Harmonic
Oscillator
Live Demonstration
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Wavelength
• The distance between successive crests, troughs, or identical parts of a wave.
•Common symbol used for
wavelength is the Greek letter - pronounced “lambda”
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Sine Curve
AmplitudeA
Wavelength Crest
Trough
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• Frequency: The number of vibrations per unit time.
• Common symbols are f and the Greek
letter - pronounced ”nu”
•Period: The time in which a vibration is completed.
•Common symbols are T and the Greek letter - pronounced “Tau”
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More on frequency
• We can talk about the frequency of a vibration or of a wave. Frequency is measured in inverse seconds, or Hertz (Hz).
•E.g..
•f = 10 cycles/sec = 10sec-1 = 10 Hz.
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Frequency and Period are related
• Frequency equals inverse Period.
•Period equals inverse Frequency.
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In symbols, this means...
f = 1/T or = 1/ and
T = 1/f or = 1/
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Examples
AM radio frequencies are measured in KiloHerts - (KHz).
The period is 1/1,000Hz = 1x10-3 sec = 1millisecond (ms)
Kilo = one thousand = 1,000 = 1x103 .
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• FM radio frequencies are measured in MegaHertz (MHz)
•The period is (1/1,000,000 Hz)=
1x10-6 sec = 1 microsecond (s).
•Mega = one million = 1,000,000 = 1x106
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More Examples• Water waves might have a
frequency of 2Hz (i.e. 2 cycles per second).
•The corresponding period is equal to:
1/f = 1/2Hz = 0.5 seconds
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• The AM and FM radio waves are examples of
• Light is another example of an
electromagnetic wave
•Electromagnetic Waves
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The water waves are examples
of Mechanical Waves
Mechanical waves require a medium in which to propagate. Electromagnetic waves do not.
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Wave Speed
• The speed with which waves pass a particular point.
•Common symbol used for
wavespeed is the letter v.
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• Wavespeed = wavelength / period
v = f
but, since we already know that frequency is the same as inverse period ( f = 1/T), then we can also write this as
v = /T
•In symbols, this is:
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A note as to why we use “v”
• The letter v is used for velocity in general.
•Velocity is speed in a specific direction.
•Velocity and speed are closely related.
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For Example• If I tell you I’m traveling at
55 miles/hour due north, I
have told you my velocity
•If I tell you I’m traveling at 55 miles/hour, I have told you my speed.
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Types of Waves
There are two types of waves
2)Longitudinal Waves.
1) Transverse Waves.
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1) Transverse Wave:
A wave in which the vibration is in a direction perpendicular (transverse) to the direction in which the wave travels.
e.g. Light waves.Waves on a string.Seismic “S”-waves.
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2) Longitudinal Wave:
A wave in which the medium vibrates in a direction parallel (longitudinal) to the direction in which the wave travels.
e.g. Sound.Seismic P-waves.
http://www.physics.ohio-state.edu/133/demo/Lwave.gif
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In a longitudinal wave, the medium has regions of compression and expansion which are along the direction of wave propagation.
Regions of expansion are also called (rarefactions)
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•
Interference
A number of different waves can add, constructively or destructively.
The superposition of two or more waves results in interference.
This is known as superposition.
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Destructive Interference:
Exactly out of Phase
Cancellation + Zero
displacement
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Constructive Interference:
In PhaseMaximum Displacement
Reinforcement
+
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•
Interference Pattern
The pattern formed by superposition of different sets of waves that produce mutual reinforcement in some places and cancellation in others.
Superposition Principle of Wave
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•
Standing Wave
A stationary wave pattern formed in a medium when two sets of identical waves pass through the medium in opposite directions.
lecture demos
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Standing Wave
V
V
V
V
Standing Wave
Incident Wave
Reflected Wave
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Beats
•
Sometimes, two waves with slightly different frequencies but the same
amplitude can form the phenomenon known as beats.
15.11 Beats
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Blue colored wave + green colored wave ==> red colored wave. Two waves with same amplitudes but slightly different frequencies.
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•
Doppler Effect
The shift in received frequency due to motion of a vibrating source toward or away from a receiver.
15.6 The Doppler Effect
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•
Bow WaveThe V-shaped wave made by an object moving across a liquid surface at a speed greater than the wave speed.
(Since the source is moving faster than the wave speed, the wavefronts pile up.)
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•
Shock WaveThe cone-shaped wave made by an object moving at supersonic speed through a fluid.
(Here, the source is moving faster than the wave speed, which is the speed of sound!!)
(Super-sonic speed)
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•
Sonic Boom
The loud sound resulting from the incidence of a shock wave.
(This is the result of the pile up of many wave fronts which produces a sonic boom)
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•
Sonic Boom
Piled up wave fronts produce a shock wave
Plane
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•
Twice the speed of sound - Mach 2
Plane
2 units
1 unit
Wave front
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The End of Chapter 19