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Standing Waves

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Standing Waves Although waves usually travel from one place to another, it is possible to make a wave stay in one place. – PowerPoint PPT presentation

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Title: 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.
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