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 .ra—ilfll
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 <!*»»'?« n«»t 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* th«»n I'xt'rut*-their movements in opposite; phascH and nothing i« pn»pngat«'«i to a ih«t«»«*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*rrtti«»n« got out of step while they ttlill remain canmd^nihltf, I^«t ii» MtijtjHwr tli«t there is a relative gain or loss of half a period while ih«- vs!»rali««ts ilii»« il««wit 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»|»i»»if»g 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, i»r ft !I>KH tlmn \ 'w*. It has been assumed throughout that r is much ]nw than /{.ation of motion is