Standing Waves

1
Standing Waves

• Although waves usually travel from one place to
  another, it is possible to make a wave stay in
  one place.

2
A wave that is trapped in one spot is called a
Standing Wave.

• It is possible to make standing waves of almost
  any kind.
• This includes,
• Water
• Sound
• And even light!
• A vibrating string is a good example of a
  standing wave.
• Vibrating strings are what make the music that we
  enjoy on a guitar or a piano.

3
Standing waves occur under a special set of
circumstances.

• Standing waves occur at frequencies that are
  multiples of the Fundamental.
• The Fundamental is the natural frequency of the
  string.
• The fundamental and multiples of its frequency
  are called, Harmonics.
• You can tell the harmonic number by counting the
  number of bumps that are found on the wave.
• These bumps are separated by collars that seem
  to cut that bump off from the next.
• These collars are called Nodes.
• The central portion of the bump where the most
  motion occurs is called the Antinode.

4
What do harmonics look like?

• Just look at the keys on a piano to see the
  different harmonics.

5
Looking at the same harmonics, describe to me the
number of nodes and antinodes that you see in
each harmonic.
6
Its also very easy to determine the frequency of
the harmonics.

• All you have to know is the initial frequency.
• If the first Bump has a frequency of 10 Hz,
  then the second bump will be at a frequency of 20
  Hz, and the third at 30 Hz, and so forth and so
  on.

Harm. Freq. (Hz) Wavelength (m) Speed (m/s) fn / f1 Wn /W1
1 400 1.60 640 1 1/1
2 800 0.800 640 2 1/2
3 1200 0.533 640 3 1/3
4 1600 0.400 640 4 1/4
5 2000 0.320 640 5 1/5
n n 400 (2/n)(0.800) 640 n 1/n
7
Now a vibrating string will move so fast that
your eye averages out the image and you see a
wave-shaped blur.

• At any one moment the string is really in only
  one place within the blur.
• The wavelength is the length of one complete S
  shape on the string.
• The higher the frequency the shorter the
  wavelength.

8
Allrighty then! I know that the majority of you
have already asked yourselves this one very
important question.

• Why are standing waves useful?
• Standing waves are useful because we can control
  their frequency and wavelength.
• Because the wave is trapped, it is easy to put
  power into it an make larger amplitudes.
• Standing Waves
• In your microwave oven, there is a device called
  a magnetron.
• Inside the magnetron is a standing wave driven by
  electricity.
• A small hole is the boundary lets a measured
  amount of the waves energy out to cook the food.
• The shape of the magnetron forces the standing
  wave to oscillate at exactly 2.4 billion cycles
  per second.
• Energy that leaks out at the same frequency is
  perfectly matched to heat the water molecules in
  food!
• Microwaves will not work on a substance that has
  no water!

9
And then there was Interference.

• Interference happens when two or more waves come
  together.
• Because there are so many waves around us they
  sometime interfere with each other, but sometimes
  they dont.
• If you remember back to the Three Sisters,
  those were the waves that didnt interfere with
  each other but built upon one another.
• This is called Constructive Interference.
• Constructive interference occurs when waves add
  up to make a larger amplitude
• Constructive Wave Interference

10
Then what is Destructive Interference.

• There is another way to launch the two pulses.
• If you make the pulses on opposite sides of a
  material something different happens.
• When the pulses meet at the middle they cancel
  each other out!
• One wants to pull the material up and the other
  wants to pull the material down.
• The result is that the wave in the material
  vanishes for a moment.
• And that moment when the wave vanishes is called,
  Destructive Interference.
• Destructive Wave Interference

11
The strange thing about destructive interference
happens after the pulses meet and the wave
vanishes.

• After the interfere. Both wave pulses separate
  and travel on their own.
• The surprising thing is that for a moment the
  middle of the material is flat and a moment later
  two wave pulses come out of the flat part and
  continue on their way.
• The important thing to remember is that waves
  still store energy, even when they interfere.

12
There is one more use of interference that I
would like to mention here.

• At the level of the atom there are some extremely
  strong waves.
• Now, because they are so random and scattered
  they mainly interfere on the destructive side of
  interference.
• But there are cases where atoms can be made to
  show a constructive interference side to
  themselves.

13
Ever hear of a MRI?

• MRI stands for Magnetic Resonance Imaging.
• This uses the constructive inference of waves to
  paint a picture of the soft tissues of the
  inner body.
• The view at the lower right is that of a torn
  rotator cuff in the shoulder.