Goal: to understand waves
Objectives:
1) To learn about Oscillations and vibrations
2) To understand the properties of Waves
3) To learn about Transverse waves
4) To understand Interference
5) To learn about how to use waves
scientifically
Wave properties
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(draw wave on board)
Waves have:
Period – how long it takes to complete wave
Frequency – how many waves you get every
second (units are 1/seconds, or Hertz)
Period = 1 / Frequency
Wavelength – distance from crest to crest or
trough to trough
Amplitude – height of the wave
Velocity – how fast the wave moves
Linear frequency vs angular
frequency
• Linear frequency (f) is how often an object
does a full pulse per second (units Hertz)
• Angular frequency (w) is how many
radians the pulse cycles through each
second (units rad/sec)
• Yes, angular velocity and angular
frequency are pretty much the same thing.
• The conversion: w = 2π f
Quick sample
• A wave has an angular frequency of 2.4
rad/sec.
• What is the linear frequency of the wave?
Transverse waves
• Transverse waves are waves that
propagate in a direction ahead, but the
wave is caused by a motion perpendicular
(aka side to side).
• An example is a string moved back and
forth.
Standing Waves
• Standing waves are waves that have
“nodes” that stay in place.
• Nodes are points that don’t move.
• For this to happen, how much my
wavelength compare to the length of my
spring/string?
Wave speed
• The velocity that waves move is called wave
speed.
• Wave speed = wavelength * frequency
• On the shore of a lake 4 waves come by every 3
seconds.
• The distance between the crests of the waves is
12 m.
• A) What is the frequency of the waves?
• B) What is the wave speed of the waves?
Another way to find speed
• On a string:
• V = (FL/m)1/2
• L is the length of string, m is the mass of the
string, and F is the tension in the string
• m/L = linear mass density = μ
• So, another way to write the equation is:
V = (F/ μ)1/2
Example from HW slightly redone
• While using a land line telephone you flick
the cord sideways.
• The cord has a mass of 0.1 kg and a
length of 1.2 meters.
• If the wave takes 0.2 sec to get to the end
of the cord find:
• A) the velocity of the wave (we have a
distance and a time…)
• B) The Tension of the phone cord
Longitudinal (compression) waves
• These are waves that compress the local
region.
• Examples of this are sound waves and
Spiral Arms in Astronomy.
Equation for a wave
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Y = A sin(kx + wt)
A is the max amplitude
X is the position
W is the angular frequency of the wave
k is the wave number of the wave
(kx + wt) is the phase of the wave
• The wavelength is set by kx = 2π
• So, wavelength = 2π/k
Interference
• If you toss two rocks at each other, they
collide.
• If two waves cross each other, they pass
through, by they do interfere at that point.
• The two waves add.
Constructive interference
• If the waves are positive at the same time
and negative at the same time they will
make a bigger wave.
• This is called constructive interference.
• Can you think of a use for this?
• When would this be a bad thing?
Destructive interference
• If the waves are opposite to each other
then when you add them you get a smaller
wave, or sometimes no wave at all.
• This is called destructive interference.
• When would this be a good thing?
• When is this a bad thing?
Scientific Use 2 - seismology
• Earthquakes are waves that pass through the
earth.
• A fault acts like my hand moving the spring back
and forth.
• Earthquakes actually cause not 1 but 2 waves.
• The P wave are compression waves and can
move anywhere.
• S waves go side to side (they do the shaking)
and can only move through solids.
What can we learn from
earthquakes?
• A lot actually.
• The first thing is that we look at the P and S
waves go through the center of the earth.
• From this we can tell that there is a liquid portion
of our core (as the S waves don’t go through
that).
• Also, different materials, and different
densities/phases have different wave speeds.
• So, if we measure how long it takes the P waves
to go in different directions through the core then
we can tell what the core is made of, and what
its temperature and densities are.
Also
• We can use smaller man made “quakes”
on the surface of the earth to find
materials such as oil.
If time
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A string has a weight attached to the end of it of unknown mass.
The string is vibrated at an angular frequency of 2 rad/sec.
The wave number (k) = 0.4 m-1
The string has a linear mass density of 0.03 kg/m.
There are 2.5 waves on the string (drawn on the board).
A) What is the wavelength of the waves?
B*) What is the length of the string?
C) What is the linear frequency of the waves?
D*) What is the wavespeed of the waves?
E*) If the tension is created by the weight at the end then what is the
size of the unknown weight (this one is a bit tricky)?
• * indicates similar to a homework question
Conclusion
• We have learned a lot about waves.
• We have learned the properties of waves.
• We have seen 2 ways of creating waves
(transverse and compression).
• We have found ways to use these waves
to arrive at scientific discoveries.