1 Solu%ons for Homework set 1 – chapters 1—5 in...
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Solu%ons for Homework set 1 – chapters 1—5 in Kinsler 1 1. 2.
Transcript of 1 Solu%ons for Homework set 1 – chapters 1—5 in...
Solu%onsforHomeworkset1–chapters1—5inKinsler 1
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11.Asteelbarofcrosssection0.0001m2and0.25mlengthisclampedatbothends.a)whatisitsfundamentalfrequencyforlongitudinalvibrations?b)whatisthefundamentalfrequencyforthesamebarbutfreeatbothends?c=sqrt(y/rho);forcommonsteelwecantakeY=200GPa=2x10^11Pa,density=7900kg/m^3,soc=sqrt(2x10^11/7900)=5030m/s.Forlongitudinalwaves,cross-sectiondoesnotmatteraslongasbaris“slender”(L>>diameter)asinthiscase.Forendsclamped,f_1=c/2L=5030m/s/0.5m=10kHzforendsfree,resultissame-differenceisthatclampedendsmustbenodes,freeendsmustbeanti-nodes,butfundamentalfhasL=lambda/2.
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