Chapter 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
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:
L
P  2
g
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
Crest
Wavelength

Trough
Amplitude
A
• 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
and
T = 1/f
or  = 1/
or
 = 1/
Examples
AM radio frequencies are
measured in KiloHerts - (KHz).
Kilo = one thousand = 1,000 =
1x103 .
The period is 1/1,000Hz = 1x10-3 sec
= 1millisecond (ms)
• FM radio frequencies are
measured in MegaHertz (MHz)
•Mega = one million
= 1,000,000 = 1x106
•The period is
(1/1,000,000 Hz)=
1x10-6 sec = 1 microsecond (s).
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
•Electromagnetic Waves
• Light is another example of an
electromagnetic wave
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
•In symbols, this is:
v = /T
but, since we already know that
frequency is the same as inverse
period ( f = 1/T), then we can also
write this as
v = f
A note as to why we use “v”
• The letter v is used for velocity
in general.
•Velocity and speed are closely
related.
•Velocity is speed in a specific
direction.
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
1) Transverse Waves.
2)Longitudinal 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.
•
This is known as superposition.
The superposition of two or more
waves results in interference.
Destructive Interference:
Exactly out of Phase
Cancellation
+
Zero
displacement
Constructive Interference:
Reinforcement
+
In Phase
Maximum
Displacement
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
Incident Wave
V
Reflected Wave
V
Standing Wave
V
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 Wave
The 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 Wave
The 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
Wave front
•
1 unit
Plane
2 units
The End of Chapter 19