# A55 Standing Wave (Fixed at Both Ends)

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:

1. NAN,
2. NANAN,
3. NANANAN,
4. NANANANAN,
5. NANANANANAN, and so on.

(N denotes a node and A denotes an antinode)

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

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

Which means that

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