A56 Standing Wave (One Free End)

This video shows the standing waves that can be formed on a string that is fixed at one end or loose at the other end.

Any standing wave that forms on this string must have a node (N) at the fixed end, and antinode (AN) at the loose end.

As such, the possible standing waves are:

  1. NA,
  2. NANA,
  3. NANANA,
  4. NANANANA,
  5. NANANANANA, and so on.

Notice that each AN corresponds to 1 quarter-wavelength segment. So

  1. NA’s wavelength is called the fundamental wavelength,
  2. NANA’s wavelength is 1/3 that of the fundamental wavelength,
  3. NANANA’s wavelength is 1/5 that of the fundamental wavelength,
  4. NANANANA’s wavelength is 1/7 that of the fundamental wavelength,
  5. NANANANANA’s wavelength is 1/9 that of the fundamental wavelength, and so on.

Which means that

  1. NA’s freq is called the fundamental, or 1st harmonic,
  2. NANA’s freq is 3x that of the fundamental, hence called the 3rd harmonic,
  3. NANANA’s freq is 5x that of the fundamental, hence called the 5th harmonic,
  4. NANANANA’s freq is 7x that of the fundamental, hence called the 7th harmonic,
  5. NANANANANA’s freq is 9x that of the fundamental, hence called the 9th harmonic, and so on.

 

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