standing waves in a pipe
blow across a tube and almost everything you put in cancels itself out. only the waves that fit the ends survive, reflecting back and forth until they stand still. the air still moves — but the pattern doesn't.
resonates at
259.8 Hz
nearest note
C4
wavelength
132 cm
pipe holds
0.5 λ
both ends open, so the air is free to swing at both — antinodes at each mouth, and the pipe holds a whole number of half-wavelengths. every harmonic fits. that's a flute.
notice the two curves are always opposites: where the air swings hardest the pressure barely changes, and where the air is pinned still the pressure swings the most. an open end is a pressure node because it's connected to a whole room that refuses to be squeezed.
the tone is built only from the harmonics this tube can hold. switch between open and closed at the same length and listen: an octave apart, and the closed one hollowed out.
why a clarinet is a bad flute
a flute is a tube open at both ends. a clarinet is about the same length but its reed end is effectively sealed. so the clarinet plays roughly an octave lower than a flute of the same size, and it skips every even harmonic on the way up — which is why overblowing a flute gives you the octave, while overblowing a clarinet jumps a twelfth instead. set the length to 66 cm and flip the ends to hear both.