Date post: | 02-Jan-2016 |
Category: |
Documents |
Upload: | madlyn-quinn |
View: | 235 times |
Download: | 10 times |
Chapter 19Chapter 19
Vibrations and Waves
• Vibration: A disturbance
“wiggle” in time.
•Wave: A disturbance in
space and time.
Oscillatory Motion
• The to-and-fro vibratory motion, such as that of a pendulum.
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:
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.
Simple Pendulum
• Under small displacements, the simple pendulum behaves as a harmonic oscillator.
•For a pendulum, the “restoring force” is usually exerted by
GRAVITY
Amplitude
• The maximum displacement from some equilibrium (mid point) position.
(Applies to both vibrations and waves.)
Mass-Spring System is Another Example of a Simple Harmonic
Oscillator
Live Demonstration
Wavelength
• The distance between successive crests, troughs, or identical parts of a wave.
•Common symbol used for
wavelength is the Greek letter - pronounced “lambda”
Sine Curve
AmplitudeA
Wavelength Crest
Trough
• 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”
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.
Frequency and Period are related
• Frequency equals inverse Period.
•Period equals inverse Frequency.
In symbols, this means...
f = 1/T or = 1/ and
T = 1/f or = 1/
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 .
• 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
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
• The AM and FM radio waves are examples of
• Light is another example of an
electromagnetic wave
•Electromagnetic Waves
The water waves are examples
of Mechanical Waves
Mechanical waves require a medium in which to propagate. Electromagnetic waves do not.
Wave Speed
• The speed with which waves pass a particular point.
•Common symbol used for
wavespeed is the letter v.
• 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:
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.
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.
Types of Waves
There are two types of waves
2)Longitudinal Waves.
1) Transverse Waves.
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.
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
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)
•
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.
Destructive Interference:
Exactly out of Phase
Cancellation + Zero
displacement
Constructive Interference:
In PhaseMaximum Displacement
Reinforcement
+
•
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
•
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
Standing Wave
V
V
V
V
Standing Wave
Incident Wave
Reflected Wave
Beats
•
Sometimes, two waves with slightly different frequencies but the same
amplitude can form the phenomenon known as beats.
15.11 Beats
Blue colored wave + green colored wave ==> red colored wave. Two waves with same amplitudes but slightly different frequencies.
•
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
•
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.)
•
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)
•
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)
•
Sonic Boom
Piled up wave fronts produce a shock wave
Plane
•
Twice the speed of sound - Mach 2
Plane
2 units
1 unit
Wave front
The End of Chapter 19