idea
Strings and pipes
A string is fixed at both ends, so the ends cannot move. The only vibrations that last are the ones that fit exactly between the two ends: one half-wave, two half-waves, three, and so on. Each of these shapes has its own frequency, 1, 2, 3… times the lowest one. The air inside a wind instrument follows the same rule with its own boundaries. A flute is open at both ends and holds all the harmonics. A clarinet is closed at one end and holds mostly the odd ones, which is part of why it sounds so different.