[1]
Nonvector derivations of the wave equation are given in Rayleigh, theory of sound, vol. 2, pp. 1–15, (Dover, 1945); P.M. Morse. Vibration and sound. 2nd ed. New York: Acoustical Society of America; 1981. p. 217–225; L.E. Kinsler, A. R. Frey, A. B. Coppens, and J. V. Sanders. Fundamentals of acoustics. 4th ed. New York: John Wiley & Sons, Inc.; 2000. p. 113–213; and other places.
[2]
A vector derivation of the wave equation is given in two papers that must be read together: W.J. Cunningham, application of vector analysis to the wave equation, J Acoust Soc Am 1950; 22:61 and R.V.L. Hartley. Note on Application of Vector Analysis to the Wave Equation. J Acoust Soc Am 1950;22:511.
[3]
If a mass of gas is chosen so that its weight ...