Embed Size (px)
Citation preview
Solu%onsforHomeworkset1–chapters1—5inKinsler 1
1.
2.
3.
5.
6.
8.
9.
10.
11.
12.2.2cont’d10.
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.
Alternate11.
13.
14.
15.
12.
16.
17.
