. Compendium of meteorology. Meteorology. SOUND PROPAGATION IN THE ATMOSPHERE 369 if the wave length L approaches the mean free path I of the molecules. Schrodinger [26] writes k = Fl/U, (26) where F =\2 7rV3[(A' - 1) AK-''- + 4 BK-'% K = Cp/ci,; A and B are constants depending on the heat conduction q of the gas, its coefficient of internal friction u, the molecular velocity c, and the mean free path Z of the molecules: q = Ac, u/c = Bd. (27) Schrodinger calculated from laboratory experiments F = ; Kolzer [18] later used F = Consequently, loss of energy E from absorption between two
. Compendium of meteorology. Meteorology. SOUND PROPAGATION IN THE ATMOSPHERE 369 if the wave length L approaches the mean free path I of the molecules. Schrodinger [26] writes k = Fl/U, (26) where F =\2 7rV3[(A' - 1) AK-''- + 4 BK-'% K = Cp/ci,; A and B are constants depending on the heat conduction q of the gas, its coefficient of internal friction u, the molecular velocity c, and the mean free path Z of the molecules: q = Ac, u/c = Bd. (27) Schrodinger calculated from laboratory experiments F = ; Kolzer [18] later used F = Consequently, loss of energy E from absorption between two points close enough to each other so that the absorption can be assumed to be constant is given by In (Ei/Ei) = - Fl D/U = - e'^'yU. (28) The factor e'''* is based on the assumption of constant temperature throughout the atmosphere, but the re- sulting mean free paths are within the limits given by the tables for the stratosphere (see Table I). Table I. Mean Free Path {I X lO'"'* cm) of Molecules at Different Levels Height above sea level (A km) 0 20 12 15 10 8 40 150 580 259 120 60 80 100 120 (a) (b) (c) (d) 1,800 14,000 2,600 830 22,000 200,000 20,000 4,400 270,000 6,160,000 260,000 36,000 3,300,000 66,000,000 1,700,000 140,000 (a) / = 10-5 e*"''. (b) [21] tentative minimum temperatures. (c) tentative standard temperatures. (d) tentative maximum temperatures (for h = 100 and 120 km during the day). If it is assumed that the distance D is 1 km, that the free path of the molecules decreases exponentially with altitude h (in km) from 10~^ cm at sea level, that the height of the homogeneous atmosphere is km, and that the wave length L is measured in meters, In L = - - ^hil- ME^/E;)]. (29) Equation (29) enables the calculation of L as a function of h for a given absorption. Results are plotted in Fig. 3, which can be used to find the height h above which waves of a given length L lose the
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