Title: Standing Waves
1Standing Waves
- Although waves usually travel from one place to
another, it is possible to make a wave stay in
one place.
2A 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.
3Standing 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.
4What do harmonics look like?
- Just look at the keys on a piano to see the
different harmonics.
5Looking at the same harmonics, describe to me the
number of nodes and antinodes that you see in
each harmonic.
6Its 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
7Now 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.
8Allrighty 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!
9And 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
10Then 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
11The 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.
12There 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.
13Ever 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.