140 Standing Wave Odd Harmonics

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 at the fixed end, and antinode at the loose end.

The simplest standing wave fulfills these conditions is the NA. (Node-Antinode) The next standing wave that can be formed is the NANA, followed by

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

Notice that each ANA corresponds to 2 quarter-wavelength segment. This means

  1. NA packs 1 quarter-wavelength along the length of the string,
  2. NANA packs 3 quarter-wavelengths along the length of the string,
  3. NANANA packs 5 quarter-wavelengths along the length of the string,
  4. NANANANA packs 7 quarter-wavelengths along the length of the string,
  5. NANANANANA packs 9 quarter-wavelengths along the length of the string, and so on.

Which means that

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

Which means that

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

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