[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 in grams is equal to its molecular weight (known to chemists as the gram-molecular weight, or the mole), then the volume of this mass at 0°C and 0.76 m Hg is the same for all gases and equals 0.02242 m3. Then R = 8.314 watt-sec per degree centigrade per gram-molecular weight. If the mass of gas chosen is n times its molecular weight, Then R = 8.314 n.
[4]
Beranek See LL. Acoustic measurements
. New York: Acoustical Society of America; 1988:49.
[5] Serway R.A, Jewett J.W.
Principles of physics: a calculus - based text
. 4th ed. Calif: Thomson Brooks/Cole, Belmont; 2006: 053449143X:550.
[6] Webster A.G. Acoustical impedance, and the theory of horns and of the phonograph.
Proc Natl Acad Sci USA
. 1919;5:275–282.
[7]
For the type of source we have assumed and no dissipation, this case breaks down for kl = nπ.
