Since the string is fixed at both ends, any standing wave that forms on the string must have nodes (N) at both ends.

As such, the possible waves are:

**N**A**N**,
**N**ANA**N**,
**N**ANANA**N**,
**N**ANANANA**N**,
**N**ANANANANA**N**, and so on.

(N denotes a node and A denotes an antinode)

–

Notice that each NAN corresponds to one half-wavelength segment. So

- NAN’s wavelength is called the fundamental wavelength,
- NANAN’s wavelength is 1/2 that of the fundamental wavelength,
- NANANAN’s wavelength is 1/3 that of the fundamental wavelength,
- NANANANAN’s wavelength is 1/4 that of the fundamental wavelength,
- NANANANANAN’s wavelength is 1/5 that of the fundamental wavelength, and so on.

–

Which means that

- NAN’s freq is called the fundamental frequency, or 1
^{st} harmonic,
- NANAN’s freq is 2x that of fundamental freq, hence called the 2
^{nd} harmonic,
- NANANAN’s freq is 3x that of fundamental freq, hence called the 3rd harmonic,
- NANANANAN’s freq is 4x that of fundamental freq, hence called the 4th harmonic,
- NANANANANAN’s freq is 5x that of fundamental freq, hence called the 5th harmonic, and so on.

### Like this:

Like Loading...

*Related*