FIGURE 6 A noctilucent (night luminous) cloud photographed over Scandinavia. Reproduced from Witt (1957) with permission of Munksgaard International Publishers Ltd., Copenhagen, Denmark. Copyright 1957 by Munksgaard International Publishers Ltd.

Since all wave phenomena involve oscillatory behavior, it is illustrative to study a simple oscillation of the atmosphere before studying its wavelike behavior. Suppose we fill an imaginary, weightless balloon with air at a given height in the atmosphere. Since the balloon is weightless the parcel will stay where it is. Now suppose we gently displace it upward. Since atmospheric density decreases with height, the parcel will weigh more than the surrounding air and will sink back toward its original position. But it will overshoot the mark, only to be slowed down and eventually forced back up by buoyancy. The parcel will oscillate about its original spot with a frequency called the Brunt-Vaisalla frequency. In a more careful analysis, a real parcel of air will cool and expand as it goes upward and compress going downward, so this effect must be taken into account, but the result is changed only in detail. In the case of an atmosphere with a constant temperature, the oscillation period can be written in the form

where g is the gravitational constant for the Earth and H is the scale height of the atmosphere. In fact, H is the distance in which the air becomes thinner by about 30 percent, about 7 km near the surface. It is of some interest that the period of a pendulum is given by the expression



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