Traveling Waves
Lecture 34
Friday. December 5
Exam 4 Average = 88.4
12
10
8
6
4
2
0
A
B
C
D
Waves
•
•
•
•
Sound
Water
Electromagnetic
Traveling versus Standing
Waves on a String
• Wave on a string-motion perpendicular to
string-pulse
t=1.34 s
t=2.05 s
Speed of a wave on a string
• Linear mass density
m

L
vSTRING 
TS

String
• Motion is perpendicular to the string and to
the direction the wave is moving. Hence a
transverse wave.
Sound
• Pressure wave, air particles move back and
forth in the direction of propagation—hence a
longitudinal wave.
vSOUND 
 kBT
M
• Speed in air at t=200 C = 343 m/s
Graphing a Wave
• For a fixed x=x0 we can plot the wave versus
time:
y(t)
t
• A “history” graph, motion at a fixed point as a
function of time.
Snapshot Graph
• For a fixed time, t=t1
y(x)
x
Sinusoidal Waves
• Any wave can be written as the sum of
sinusoidal waves—Fourier
• y depends on x and t
– In one period t, wave goes through one oscillation
t 

y (t )  A cos  2 
 T
Wave goes through one oscillation if we
change x by one wavelength ( a wavelength is
the period In space.)
x

y ( x)  A cos  2 
 
Putting these together:
  x t 
y ( x, t )  A cos  2    
   T 
For a wave moving to the right, plus x-direction
Moving to the left, –x direction
  x t 
y ( x, t )  A cos  2    
   T 
How many waves pass a point in one
second?
f
How long is this train of waves?
f
Thus
f v
Problem 15.13
• The motion detector used in physics lab sends
out 40 kHz ultrasonic pulses. A pulse goes
out, reflects of the object being measured,
and returns to the detector. The lab
temperature is 200 C.
• A) What is the wavelength?
• B) time for a round trip to an object 2.5m
away?
Monday
• 15: 4-6 Sound and Light
• Problems 15: 1, 4, 7, 13, 15, ,17, 18