SEICHE AND HARMONICS

Any child who lives in a house with a bathtub knows about seiche (pronounced “saysh”). Any enclosed or semienclosed body of water can be made to slosh back and forth at a rate that depends on the size and shape of the container. In a bathtub, this sloshing can be set up with a period of 1 or 2 seconds. Give the water a little push, and then another, and then another. Keep this up at a certain regular repetitive rate, and soon there is water all over the bathroom. The same thing can happen in a swimming pool during an earthquake, although the period is longer. When waves moving in opposite directions collide, the peaks and troughs are exaggerated (Fig. 1).
Harmonics are familiar to anyone who plays a musical instrument such as a clarinet, flute, trumpet, or trombone. If you can blast out a note with certain keys pressed or with the slide at a given position, then if you tighten your lips enough, you can sound a note one octave higher. The higher note is the second harmonic of the first note. The chamber of the instrument contains twice as many wave peaks and valleys at the higher note as compared with the lower note. If you’re a virtuoso, you might get the instrument to toot at three times the original, or fundamental, frequency. This is the third harmonic. Mathematically, there is no limit to how far this can go (Fig. 2). When the frequency of one wave is a harmonic of the frequency of another wave, the two waves are said to be harmonically related.

Fig. 1. When waves collide, the effects are magnified.

Fig. 2. Resonant effects occur at wavelengths that are wholenumber fractions of the wavelength of the fundamental.