Sound Standing Waves

In the brass and woodwinds there are tubes in which standing waves occur, and certain frequencies are possible. A pipe organ has one pipe for each note; the length determines the frequency. In the horns and woodwinds, the frequency is determined by the distance from the mouthpiece to the first opening. We will look into how these things work in terms of a special case: the long thin tube. Fat horns are a little different but not a whole lot, so this theory is a reasonable first approximation.

All you really need to know is that there is an antinode (maximum vibration) at an open end and a node (no vibration) at a closed end. This alone determines the possible frequencies. In the sketches below, the double arrows represent antinodes and the dots = nodes. The first three show the longest possible wavelengths (lowest possible frequencies) in a pipe open at one end; the next three are open at both ends. In truth, the antinode at the open end is a little beyond the end of the tube, so we are stuck with a theory that is almost right.

In terms of speed of sound v and length of tube L, you can now find the frequencies. (Recall f = v/l .)Now you probably figure that when you blow across the top of a pop bottle, the note you get can be found by this same reasoning. Very good try, but wrong. The long thin tube model is no good for a tube that widens like that, so go back to the main poop on vibrations and waves and look for the Helmholtz resonator, or go there directly.

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