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:

**NA**,
**N**AN**A**,
**N**ANAN**A**,
**N**ANANAN**A**,
**N**ANANANAN**A**, and so on.

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

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

–

Which means that

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

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