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Full text of "Scientific Papers - Vi"

290                               MUTUAL  INFLUENCE  OF   RESONATORS
and for the pressure due to it at the surface of the first vibrator
The equation of motion for pl is accordingly
fJ^n        .railfll
and that for pt differs only by the interchange <>f pt and />,,    Attuning that both pl and pa are as functions of the tinn- proportional tt> t>iHtt wr #!  t.
determine n
^/-] - ^   H .
or approximately
"
If, as before, we take n  p + iq,
We may observe that the reaction of the rudghbour <!*'? nt tlwtiirb thi-frequency if cos kR  Q, or the damping if Hin A'/<!  0. Whrti A*/f IM wnall, the damping in one alternative diHappwim Thu two vibrator* thn I'xt'rut*-their movements in opposite; phascH and nothing i pnpngat'i to a iht*i*,
The importance of the diaturbantH* of frtHjuoncy in (5f>)rariii**t |M cKtttimti'ii without regard to the damping. The (juoHtiou is whi'th-r th two vil*rrttin got out of step while they ttlill remain canmd^nihltf, I^t ii MtijtjHwr tlit there is a relative gain or loss of half a period while ih- vs!ralits ilii ilwit in the ratio of e : 1, vi%. in the Lime denoted prvvioUHJy hy T, w that
Calling the undisturbed values of p and i/ roH|wctivHly /' atui Q> mid Hf|iifg kR to be small, we have
P
in which QjP = 2frcrk)A/M'. According to thi standard th tltHturtuuir<* f frequency becomes important only when k/t< I fir, ir ft !I>KH tlmn \ 'w*. It has been assumed throughout that r is much ]nw than /{.ation of motion is