ABSTRACT
As derived in Appendix C, the physical equation for the air pressure P in an ideal cylindrical tube, with length much greater than its width, is:
d 2P / dx2 = (l / c 2)(d 2P / dt2) ( l l . l )
“But wait,” you might say, “That’s just string Equation lO.l with string displacement y replaced by air pressure P!!!” And I would reply, “BINGO!!!” It’s the same wave equation, and the solution has the same form:
P(x, t) = Pt (t + x/c) + Pr(t - x/c) (ll.2 )
In fact, if you find a nice long piece of pipe and slap the end, you’ll get a sound very much like a simple damped plucked string.