A wave is a wave is a wave
An introduction to waves
What are some types of waves?
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Water
Sound
Light
Matter
Sports fans
Earthquakes/seismological
Hand?
What distinguishes waves?
• Water, Sound, Light, Sports Fans, quakes
• Information moves without individual
particles carrying it
What is a wave? - Webster says...
• a moving ridge or swell [on a surface of water]
• a swell, surge, or rush
• any surging or progressive movement resembling
a wave of the sea
• Physics. a progressive disturbance propagated
from point to point in a medium or space without
progress or advance by the points themselves
How is a wave useful to IT?
• the method of transmitting
information/energy/etc. from point A to
point B without individual objects traveling
between the points
Transverse waves
• Water wave: water moves up and down,
wave moves toward shore
• Rope: string moves up and down, wave
moves toward end
• Sports fans: fans rise and sit, wave moves
around stadium
• Electromagnetic (light): fields vary in a
direction perpendicular to motion
Longitudinal waves
• Slinky: Coils compressed and released
create wave in direction of compression
• Sound: Air compresses in direction of
motion, but molecules don’t travel from
source to ear
The sinusoidal (in space) “wave”
• One wavelength takes 2p radians
-f
• Described by
AA A
A=Amaxcos(2px/l)
l
A=Amaxsin(2px/l)
A=Amaxcos(2px/l + f)
x
The sinusoidal (in time) “wave”
• A cycle completes one “period” in 2p
A
radians
T
• Described by
A=Amaxcos(2pt/T+f)
A=Amaxsin(2pt/T +f)
t
Wave vocabulary
• wavelength l = distance per cycle
• wave number k = radians per distance
2p/l = rad/cycle (cycle/m) = rad/m = k
• period T = time per cycle
• angular frequency w = radians per second
2p/T = rad/cycle (cycle/s) = rad/s = w
• frequency f = number of cycles per second
f = cycles/second = 1/(second/cycles) = 1/T
• Speed v = distance per time; wave travels l in T
v = l/T
The traveling wave
• A wave varies in both space and time:
– At one location, the amplitude varies in time
– At one time, the amplitude varies in space
• A sinusoidal wave moving toward positive x is
described by
A = Amaxcos(kx – wt + f)
• A sinusoidal wave moving toward negative x is
described by
A = Amaxcos(kx + wt + f)
Animation of traveling waves
Do the Before You Start part of
the activity
Think about the questions by yourself for ~5
minutes, then work with your assigned group
to answer the questions. You should finish in
about 15 more minutes.
Each group member should fill out his or her
own activity sheet.
Do We All Agree?
• What is the frequency of the wave?
• How can we sketch a graph of the wave without
resorting to graphing calculators/software?
• How does this graph change when we change the
phase constant?
• What are the differences between a graph of V vs.
t and a graph of V vs. x?
Do the rest of the activity
Your instructor will point out a few features of
the equipment. After this has been done, work
with your assigned group to complete the
activity. You should finish in ~40 minutes.
What have we learned today?
• Waves transmit information between two points without
individual particles moving between those points
• Transverse Waves oscillate perpendicularly to the direction
of motion
• Longitudinal Waves oscillate in the same direction as the
motion
• The spatial dependence of periodic waves can be described
by either the wavelength l or the wave number k, which
are related.
• The time dependence of periodic waves can be described
by either the period T, the angular speed w, or the
frequency f, which are all related.
What else have we learned today?
• Any traveling sinusoidal wave may be
described by
y = ym sin(kx  wt + f)
 f is the phase constant that determines
where the wave starts.
Before the next class, . . .
• Read the Assignment on Waves found on
WebCT
• Read the Assignment on Reflection and
Refraction using on-line tutorial (start from
WebCT Contents)
• Do Reading Quiz 1 which will be posted on
WebCT by Tuesday.