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
- NA,
- NANA,
- NANANA,
- NANANANA,
- NANANANANA, and so on.
Notice that each ANA corresponds to 2 quarter-wavelength segment. This means
- NA packs 1 quarter-wavelength along the length of the string,
- NANA packs 3 quarter-wavelengths along the length of the string,
- NANANA packs 5 quarter-wavelengths along the length of the string,
- NANANANA packs 7 quarter-wavelengths along the length of the string,
- NANANANANA packs 9 quarter-wavelengths along the length of the string, and so on.
Which means that
- NA’s wavelength is called the fundamental wavelength,
- NANA’s wavelength is 3x as short as that of NAN’s,
- NANANA’s wavelength is 5x as short as that of NAN’s,
- NANANANA’s wavelength is 7x as short as that of NAN’s,
- NANANANANA’s wavelength is 9x as short as that of NAN’s, and so on.
Which means that
- NA’s frequency is called the fundamental frequency, or 1st
- NANA’s frequency is 3x that of NAN’s, hence called the 3rd harmonic,
- NANANA’s frequency is 5x that of NAN’s, hence called the 5th harmonic,
- NANANANA’s frequency is 7x that of NAN’s, hence called the 7th harmonic,
- NANANANANA’s frequency is 9x that of NAN’s, hence called the 9th harmonic, and so on.