383.
FURTHER CALCULATIONS CONCERNING THE MOMENTUM OF PROGRESSIVE WAVES.
[Philosophical Magazine, Vol. xxvn, pp. 436—440, 1914.]
THE question of the momentum of waves in fluid is of interest and has given rise to some difference of opinion. In a paper published several years ago* I gave an approximate treatment of some problems of this kind. For a fluid moving in one dimension for which the relation between pressure and density is expressed by
P=/0>)> ..............;.............•.......(!)
it appeared that the momentum of a progressive wave of mean density equal to that of the undisturbed fluid is given by
in which p0 is the undisturbed density and a the velocity of propagation. The momentum is reckoned positive when it is in the direction of wave-propagation.
For the " adiabatic " law, viz. :
.............................. (3)
Pol PO
In the case of Boyle's law we have merely to make 7 = 1 in (5).
For ordinary gases 7 > 1 and the momentum is positive ; but the above argument applies to all positive values of 7. If 7 be negative, the pressure would increase as the density decreases, and the fluid would be essentially unstable. • : . •
* Phil. Hag. Vol. x. p. 364 (1905) ; Scientific Papers, Vol. v. p. 265. 1-00 1 -546 1-60 0-064