Standing Waves, Medium Fixed At Both Ends
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Here is an animation showing the standing wave patterns that are produced on a medium such as a string on a musical instrument. This type of medium would be said to be fixed at both ends, that is, held motionless at both ends.
Basic operation:
- You can select which harmonics, 1st to 5th, which you want to see by checking the appropriate checkbox.
- The sum of all the harmonics is always shown. It is in white.
- If you click the 'See' checkbox you will see the separate harmonics drawn behind the white sum.
- The 'Slow' checkbox makes the animation run five times slower for careful study.
When a string on an instrument is plucked, vibrations, that is, waves, travel back and forth through the medium being reflected at each fixed end. Certain sized waves can survive on the medium. These certain sized waves will not cancel each other out as they reflect back upon themselves. These certain sized waves are called the harmonics of the vibration. They are standing waves. That is, they produce patterns which do not move.
On a medium such as a violin string several harmonically related standing wave patterns are possible. The first five of them are illustrated above. It is important to understand that for any one given medium fixed at each end only certain sized waves can stand. We say, therefore, that the medium is tuned.
The first pattern has the longest wavelength and is called the first harmonic. It is also called the fundamental.
The second pattern, or second harmonic, has half the wavelength and twice the frequency of the first harmonic. This second harmonic is also called the first overtone. This can get confusing with the second member of the harmonic group being called the first member of the overtone group.
The third harmonic, or pattern, has one third the wavelength and three times the frequency when compared to the first harmonic. This third harmonic is called the second overtone.
The other harmonics follow the obvious pattern regarding wavelengths, frequencies, and overtone naming conventions described in the above paragraph.
Depending upon how the string is plucked or bowed, different harmonics can be emphasized. In the above animation all harmonics have the same maximum amplitude. This is for purposes of illustration. Actually, the higher harmonics almost always have maximum amplitudes much less than the fundamental, or first harmonic.
It is the fundamental frequency that determines the note that we hear. It is the upper harmonic structure that determines the timber of the instrument.
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