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. It’s 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 2
800
0.800
1/2 3
1200
0.533
1/3 4
1600
0.400
1/4 5
2000
0.320
1/5 n
n * 400
(2/n)*(0.800)
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 wave’s 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 don’t.
If you remember back to the “Three Sisters,” those were the waves that didn’t 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.