Equação de onda: equações diferenciais na descrição do modelo oscilatório em uma e duas dimensões.

Abstract

This workischaracterizedasapurebasicbibliographicalresearch,ofexploratorycharacter where wepresent,throughphysicalexamples,ananalysisinthedescriptionsof"Mechanical Waves"specificallywavesthatpropagatealongaropeandamesh;foreachcase,thedevelopment is performedbythemediuminwhichthewavepropagates.Mostofthepropertiesofmechanical wavesapplytoalltypesofwaves,suchaselectromagneticwavesthatarepresentinthewhich we useinourlives,namely,television,radio,theinternet,microwaveoven,telephone,among others. Moreover,mechanicalwavesappearinourdailylivesas:seawaves,soundwavesand seismic waves.ThetextinwhichwepresentourresearchbeginswithsomeconceptsDifferential Equations, thenthephysicalconceptsaretreated,throughconstructionsanddefinitionsthatstart from theHarmonicMovementuntiltheyreachthedescriptionsofanundulatingmovement. From physicalconsiderations,theequationthatmodelsthewavepropagationalongastringand a mesh,one-dimensionalandtwo-dimensional,respectively,isdeduced.Usingthemethodof separation ofvariablesweobtainthesolution,inwhichasummationofsinusoidalfunctions appears andwhentheequationissolvedforaspecificproblem,specificconditions,thesum convergestoafunctionthatrepresentstheundulatorymovementofthisproblem.Thiswork allowedadeepeninginthescientificknowledgeinherenttothedifferentialequations,especially the partialdifferentialequationsthatwerenotstudiedbyundergraduatetudentsinMathematics, in addition,wewereabletoanalyzeanimportantphysicalapplicationofsuchequations.