Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/423

the fluid within the box, i.e., relatively to the box, can take place, and hence such a wave train possesses no momentum.

It follows that if the wave train have an excess of compression or rarefaction so that its mean density is greater or less than that of the undisturbed fluid (the condition of the particles returning to their initial positions being departed from), momentum will be carried positive or negative, as the case may be, exactly as represented by the excess or deficit of density in the wave train.

Thus the momentum carried by any sound wave is a measure of and is measured by the displacement of matter by that sound wave, and if the displacement is zero the momentum is zero.^[1]

The question of momentum carried by wave motion is frequently
Fig. 160. regarded from the point of view of pressure developed, that is, the pressure produced in the fluid by the communication of momentum at reflection etc. This point of view is not without interest.

Taking first the case of a gas obeying Boyle's law, i.e., ${\frac {P}{\rho }}=$ constant; the mean pressure of the whole of the space can undergo no change, for $P/\rho$ is constant for each small element throughout the region, and the integration of $\rho$ being constant (since the whole mass of fluid in the enclosure is unchanged), the integration of $P$ throughout the enclosure is also unchanged.

1. There is some want of harmony between this result and the conclusions of many eminent authorities, see Larmor. Encycl. Brit., xxxii., p. 121 b; Rayleigh. Phil. Mag., vol. iii., p. 338, 1902; and Poynting, l.c. ante. Rayleigh has amended his conclusions somewhat in a subsequent communication, l.c. ante.

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