... TransientExcitationTransientexcitationofthevocaltractoccurswheneverpressureisbuiltupbehindatotalclosureofthetractandsuddenlyreleased.Thissuddenreleaseproducesastep-functionofinputpressureatthepointofrelease.Theoutputvelocityisthereforeproportionaltotheintegraloftheimpulseresponseofthetractfromthepointofreleasetothelips.Inthefrequencydomain,thisisjustPr/stimesthetransferfunction,wherePristhestepchangeinpressure.Hence,thevelocityatthelipsmaybecomputedinthesamewayasinthecaseofturbulentexcitation,withPnreplacedbyPr/s.Inpractice,thisstepexcitationisusuallyfollowedbythegenerationoffricativenoiseforashortperiodafterreleasewhentheconstrictionisstillnarrowenough.Sometimes,iftheglottisisalsobeingconstricted(e.g.,tostartvoicing)someaspirationmightalsoresult.44.5 ... specifying the positions of the articulators. Thecoordinatesused to describe the shape are labeled in the figure. They are the position of the tongue center, the radius of the tongue body, the position ... (44.4a)Itisimportanttonotethatinderivingtheseequationswehaveretainedonlyfirstordertermsinthefluctuatingquantitiespandu.Inclusionofhigherordertermsgivesrisetononlinearequationsofpropagation.Byandlargethesetermsarequitenegligibleforwavepropagationinthevocaltract.However,thereisonesecondorderterm,neglectedinEq.(44.1),whichbecomesimportantinthedescriptionofflowthroughthenarrowconstrictionoftheglottis.InderivingEq.(44.1)weneglectedthefactthatthesliceofairtowhichtheforceisappliedismovingawaywiththevelocityv.Whenthiseffectiscorrectlytakenintoaccount,itturnsoutthatthereisanadditionaltermρv∂v∂xappearingonthelefthandsideofthatequation.ThecorrectedformofEq.(44.1 )is ∂∂xp+ρ2(u/A)2=−ρddtuA.ψ...