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Lecture 19 Purdue University, Physics 220 1
Lecture 19
Waves
PHYSICS 220
Lecture 19 Purdue University, Physics 220 2
What is a Wave
• A wave is a disturbance that travels away from its
source and carries energy.
• A wave can transmit energy from one point to
another without transporting any matter between
the two points.
• Examples:
– Stadium waves (people move up & down)
– Water waves (water moves up & down)
– Sound waves (air moves back & forth)
– Seismic waves (earth moving up & down)
– Electromagnetic waves (what moves ??)
Lecture 19 Purdue University, Physics 220 3
Why are Waves Important?
• Transport energy from one place to another
– Electromagnetic waves transport energy
(electromagnetic energy in the form of light) from the
Sun to the Earth.
– Sound waves transport energy from speakers to our
ear drums.
• In waves, energy is transported over large
distances, but matter is not.
Power
• The power carried by a wave equals the energy
emitted by the source (and carried away by the
wave) per unit time. [watts]=[joules/second]
Lecture 19 Purdue University, Physics 220 4
Lecture 19 Purdue University, Physics 220 5
Intensity
• Average power per unit area carried by the wave
past a surface which is perpendicular to the
direction of propagation of the wave.
• For spherical waves, the intensity decreases with
distance:
• Unit: W/m2
• I ! A2
I =P
4!r2
Plane wave
• Light produced by laser good example
• Intensity does not change with distance from the
source.
Lecture 19 Purdue University, Physics 220 6
Demo 1S - 16
Circular waves --- water waves
Longitudinal waves --- sound
Transverse -- light
For frequency watch
one point
For wavelength
look at one time
For velocity watch
one peak
Lecture 19 Purdue University, Physics 220 8
• Longitudinal: The medium oscillates in the same
direction as the wave is moving.
– Sound
– Slinky
• Transverse: The medium oscillates perpendicular to the
direction the wave is moving.
– Water (more or less)
– Slinky
Types of Waves
Lecture 19 Purdue University, Physics 220 9
•http://www.youtube.com/watch?v=UHcse1jJAto&feature=
related
•http://www.youtube.com/watch?v=aguCWnbRETU&featur
e=related
•http://www.youtube.com/watch?v=XA5XW0sGN_I&featu
re=related
•http://www.youtube.com/watch?v=g49mahYeNgc&feature
=related
Lecture 19 Purdue University, Physics 220 10
Waves on a String
velocity =T
µ
µ = linear mass density =m
L
T = Tension
Lecture 19 Purdue University, Physics 220 11
Question
Suppose that a longitudinal wave moves along a Slinky
at a speed of 5 m/s. Does one coil of the slinky move
through a distance of five meters in one second?
A) Yes
B) No
Lecture 19 Purdue University, Physics 220 12
Harmonic Wavesy(x,t) = A sin("t – kx)
A = Amplitude= Maximum
displacement of a point on the
wave
# =Wavelength: Distance
between identical points on the
wave
T=Period: Time for a point on thewave to undergo one completeoscillation.
f = frequency =1/T
" = angular frequency= 2$/T
k = wave number = 2$/#
v =
!
T= ! f =
"
k
Lecture 19 Purdue University, Physics 220 13
! Period: The time T for a point on the wave to undergo one complete oscillation.
! Speed: The wave moves one wavelength # in one period T so its speed is v = # / T.
Period and Velocity
v =
!
T= ! f = 2" f( )
!
2"=#
kLecture 19 Purdue University, Physics 220 14
Harmonic Waves Exercisey(x,t) = A cos("t –kx)
Label axis and tic marks for a graph
showing an observation of the wave
y(x,t) = 2 cos(4t –2x) at x=0.
Recall: T = 2 $ /"
t
+2
-2
T = 2 $ / " = 2 $/ 4 = 1.58 s
$ / 2$/4 3$/4
What is the period of this wave?
What is the
velocity of this
wave?
v = "/k= 4/2 m/s=2m/s
Lecture 19 Purdue University, Physics 220 15
• The speed of a wave is a constant that depends only on the
medium, not on amplitude, wavelength or period (similar to
SHM)
# and T are related !
# = v T or # = 2$ v / " (since T = 2$ / " )
or # = v / f (since T = 1/ f )
• Recall f = cycles/sec or revolutions/sec
" = 2$f = radians/second
• Intensity I ! A2
v = # / T
Wave Properties
Lecture 19 Purdue University, Physics 220 16
# – wavelength: distance between crests (meters)
T – period: the time between crests passing fixed location (seconds)
v – speed: the distance one crest moves in a second (m/s)
f – frequency: the number of crests passing fixed location in one
second (1/s or Hz)
" – angular frequency: =2$f (rad/s)
Wave Description
v =
!
Tf =
1
Tv = ! f
Lecture 19 Purdue University, Physics 220 17
Direction
%t
A wave y = A cos("t - kx) travels in +x direction
A wave y = A cos("t + kx) travels in -x direction
y(x,t) = Acos(!t " kx)
k !1
"
! "1
T
!t " kx = const !#t " k#x = 0
#x
#t=!
k
Lecture 19 Purdue University, Physics 220 18
The wavelength of microwaves generated by a microwaveoven is about 3 cm. At what frequency do these wavescause the water molecules in your burrito to vibrate?
A) 1 GHz B) 10 GHz C) 100 GHz
1 GHz = 109 cycles/sec
The speed of light is c = 3x108 m/s
Exercise
Lecture 19 Purdue University, Physics 220 19
! Recall that v = #f
1 GHz = 109 cycles/sec
The speed of light is c = 3x108 m/s
H H
O
Makes water molecules wiggleMakes water molecules wiggle
Exercise
f =
v
!=
3 " 108 m s
.03m= 1010 Hz = 10GHz
Lecture 19 Purdue University, Physics 220 20
Superposition Principle
• When two or more waves pass through the same
region the actual displacement is the sum of the
separate displacements.
• If two waves pass through the same region they
continue to move independently.
!y (x,t) = y
1(x,t) + y
2(x,t)
Lecture 19 Purdue University, Physics 220 21
Superposition
Lecture 19 Purdue University, Physics 220 22
Wavelength: The distance # between identical points on the wave.
Amplitude: The maximum displacement A of a point on the wave.
Amplitude A
A
y(x,t) = A cos("t –kx)
Angular Frequency ": " = 2 $ f
x
y
Wave Number k: k = 2 $ / #
Recall: f = v / #
Mathematical Description
#
Wavelength
Lecture 19 Purdue University, Physics 220 23
Wave Speed
A wave y = A cos("t - kx) travels in +x direction
A wave y = A cos("t + kx) travels in -x direction
Phase:
y(x,t) = Acos(!t " kx)
!t " kx = const !#t " k#x = 0
#x
#t=!
k= v