https://www.youtube.com/watch?v=BAZtrSAmeIQ&t=1s
•
•
•
•
result from periodic disturbance
same period (frequency) as source
Longitudinal or Transverse Waves
Characterized by
1
f 

– amplitude (how far do the “bits” move from their
equilibrium positions? Amplitude of MEDIUM)
– period or frequency (how long does it take for each “bit” to
go through one cycle?)
– wavelength (over what distance does the cycle repeat in a
freeze frame?)
f
– wave speed (how fast is the energy transferred?) v 

Wave speed: Depends on Properties of the Medium:
Temperature, Density, Elasticity, Tension, Relative Motion
vf
f 
Wavelength and Frequency are Inversely related:
The shorter the wavelength, the higher the frequency.
The longer the wavelength, the lower the frequency.
3Hz
5Hz
v

Transverse Wave
• A traveling wave or pulse that causes the elements of
the disturbed medium to move perpendicular to the
direction of propagation is called a transverse wave
Longitudinal Wave
A traveling wave or pulse that causes the elements of the disturbed
medium to move parallel to the direction of propagation is called a
longitudinal wave:
Pulse
Tuning Fork
Guitar String
Types of Waves
Sound
String
Most waves are spherical!
We still represent them as 2D
https://www.youtube.com/watch?v=MwsGULCvMB
k
Wave PULSE:
•
•
•
•
traveling disturbance
transfers energy and momentum
no bulk motion of the medium
comes in two flavors
• LONGitudinal
• TRANSverse
Traveling Pulse
• For a pulse traveling to the right
– y (x, t) = f (x – vt)
• For a pulse traveling to the left
– y (x, t) = f (x + vt)
• The function y is also called the wave
function: y (x, t)
• The wave function represents the y
coordinate of any element located at
position x at any time t
– The y coordinate is the transverse position
• If t is fixed then the wave function is
called the waveform
– It defines a curve representing the actual
geometric shape of the pulse at that time
Traveling Pulse
Wave Form
Space Snap Shots
@ t  0 s,
2
y ( x, 0) 
( x) 2  1
@ t  1s,
2
y ( x,1) 
( x  3)2  1
@ t  2 s,
2
y ( x, 2) 
( x  6)2  1
2
y ( x, t ) 
( x  3t )2  1
Time Plot: History
One position
Changing in time
2
y ( x, t ) 
( x  3t )2  1
@ x  5,
2
y (5, t ) 
(5  3t )2  1
Problem on next Quiz
• Use excel to generate plots
An Alternative Look at a Traveling Wave
© 2013 Pearson Education, Inc.
Slide 20-32
Snapshot Graph
 A graph that shows the wave’s displacement as a
function of position at a single instant of time is
called a snapshot graph.
 For a wave on a
string, a snapshot
graph is literally a
picture of the wave
at this instant.
© 2013 Pearson Education, Inc.
Slide 20-29
One-Dimensional Waves
 The figure shows a
sequence of snapshot
graphs as a wave pulse
moves.
 These are like successive
frames from a movie.
 Notice that the wave pulse
moves forward distance
x = vt during the time
interval t.
 That is, the wave moves
with constant speed.
© 2013 Pearson Education, Inc.
Slide 20-30
History Graph
 A graph that shows the wave’s displacement as a function of
time at a single position in space is called a history graph.
 This graph tells
the history of that
particular point in
the medium.
 Note that for a
wave moving
from left to right,
the shape of the
history graph is
reversed
compared to the
snapshot graph.
© 2013 Pearson Education, Inc.
Slide 20-31
Example 20.2 Finding a History Graph From
a Snapshot Graph
© 2013 Pearson Education, Inc.
Slide 20-35
QuickCheck 20.3
This is a snapshot graph at
t = 1 s of a wave pulse
traveling to the right at 1 m/s.
Which graph below shows the
wave pulse at t = –1 s?
A.
C.
B.
D.
© 2013 Pearson Education, Inc.
Slide 20-36
QuickCheck 20.3
This is a snapshot graph at
t = 1 s of a wave pulse
traveling to the right at 1 m/s.
Which graph below shows the
wave pulse at t = –1 s?
A.
C.
B.
D.
© 2013 Pearson Education, Inc.
Slide 20-37