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19. 20. 21. 22. 23. 24. 25. 1. The Wirbelrohr’s Roar lifetime of about 15 minutes. Positrons (from proton decay) and electrons would presumably combine and mutually annhilate. There should be nothing left, then, except electromagnetic radiation and neutrinos. Whether hot or cold, such a universe ought to quality as a hellish place. The mean speed v (technically, the root-mean-square speed) of molecules of mass M can be estimated by equating the mean molecular kinetic energy –12 Mv2 and mean thermal energy –23 kT; thus, v ϳ ÷kT/M.
For example, if the bottle were of soft plastic, then a gentle deformation by squeezing would damp out the fundamental tone. Why? Is this the ineluctable consequence of broken cylindrical symmetry? No, for hard-glass bottles of highly elliptical cross section render strong fundamental tones. ) The simple resonator model does not explain this. On the other hand, one might ask why the LC circuit model works as well as it does. In a puzzling reversal of expectations, I was initially astonished to discover that supposedly more sophisticated mathematical models of acoustic resonators that treated the bottle as a 38 2.
17b), of Model Two. For ﬁnite z0, however, integration of Eq. 18) are outwardly quite dissimilar, their kinship becomes apparent when the representation of an exponential as a limiting process [Eq. 19)] is again recalled. If the parenthetical expression on the right-hand side of Eq. 23) were recast as [1 - (h0/z0)(h/h0)](z0/h0)-1, then it would have the approximate value of e-h/h0 if z0/h0 were sufﬁciently large so that Comedy of Errors: What Every Aeronaut Needs to Know 45 -1 in the exponent could be neglected.