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10. If we assume produced that n is for a long time very large that is, if sound is we may take the limiting value 1,000 900 800 XTOO 5 600 500 c 400 300 200 100 1 2 3456 7 8 9 10 11 20 12 13 14 IS 16 17 ia 19 vf FIG. 20. Growth of average intensity of sound in tube with partially absorbent ends. (1) Emission and absorption assumed continuous. (2) Discontinuous emission and absorption. of the I/a, sum of the series as n increases indefinitely, Total energy in steady state and which is and we have for the steady-state energy density = JTJ we have this total energy divided by the volume, El/caV.
Compressional plane wave reflected to the left. FIG. 6. Stationary wave resultant of Figs. 5a and 56. wave length of the wave motion and is denoted letter X. the Greek by The line A shows the positions of each of the particles the first particle, having made a at the instant that P called the > complete vibration, is in its equilibrium position and is According to the conception of the kinetic theory of gases, the molecules of a gas are in a state of thermal agitation, and the pressure which the gas Here for the purpose exerts is due to this random motion of its molecules.
40, and 6 is the temperature on the absolute scale. 44. Expanding the by the binomial theorem and we have neglecting the higher powers of 50/0 ACOUSTICS AND ARCHITECTURE 24 Obviously the temperature fluctuations in a sound wave are extremely small too small, in fact, to be measurable; but the fact of thermal changes is of importance when we come to consider the mechanism of absorption of sound by porous bodies. Numerical Values. The qualitative relationships between the various phenomena that constitute a sound wave having been 'dealt with, it is next of interest to consider the order of magnitude All values of the quantities with which we are concerned.