Standing Waves--One Fixed/Closed EndStanding Waves--One Fixed/Closed End
This shows longitudinal standing waves, such as in sound waves in a pipe open at one end only. The spots are representative regions of air (not really molecules, whose high-speed random motion is not shown). The top wave is the fundamental (longest wavelength allowed), or first harmonic. It has a displacement antinode at its open end and a displacement node at its closed end. From a place where a wave's displacement is largest to the closest place where it's always zero is a quarter-wavelength, so the pipe "holds" one-quarter wavelength. The next two waves show the next two harmonics, the third and the fifth. The pipe holds, respectively, three and five quarter-wavelengths, and shorter wavelengths correspond to higher frequencies--the frequencies are three and five times the fundamental.
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Standing Wave (closed) |