IMÁGENES DE CHLADNI
MAITRELLIS LOZANO ANNY BAENA JORGE GNECCO HAROL BONILLA
BRENDA RODRIGUEZ
LABORATORIO FÍSICA CALOR – ONDAS UNIVERSIDAD DE LA COSTA, CUC. FACULTAD DE INGENIERÍA BARRANQUILLA 201 TABLA DE CONTENIDO
!"#. INTRODUCCIÓN
3
1. PLANTEAMIENTO DEL PROBLEMA
4
2. JUSTIFICACIÓN
5
3. OBJETIVOS
6
3.1 OBJETIVO GENERAL
6
3.2 OBJETIVOS ESPECIFÍCOS
6
4. METODOLOGÍA
7
5. IMÁGENES DE CLADNI
!
6. PREDISE"O # MONTAJE
12
7. RECURSOS A EMPLEAR
14
!. PRESUPUESTO PRELIMINAR
15
$. CRONOGRAMA DE ACTIVIDADES
16
BIBLIOGRAFÍA
17
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
1. !LANTEAMIENTO DEL !ROBLEMA E' +8'&(/ &% @9 0+%-& &% '/ *&(+/0-% *& -(<&%& +*)0-*/ + +%*/ &/0-+%/-/ &% *+ *-(&%-+%& 8//*+ &% &' &&-(&%+ *& C:'/*%-. E' +8?&-,+ & '/ ,-)/'-;/0-% *& '+ (+*+ +-+ *& ,-8/0-% *& )%/ '/0/ 0)/*/*/. P// &''+ & :/0& ,-8/ / *->&&%& >&0)&%0-/ )%/ '/0/ (&'-0/ 0)/*/*/9 &+',+&/%*+ 0'+)+ *-0+ + 8-0/8+%/+ *& +*-+ +8& &''/ & +8&,/% '+ /+%& '@%&/ %+*/'& )& & >+(/% &% '/ (-(/9 0+&+%*-=%*+& 0/*/ /% 0+% )% (+*+ +-+ *& ,-8/0-% *& '/ '/0/.
2. JUSTIFICACI$N E >)%*/(&%/' &/'-;/ &' *-&+9 (+%/?& &&%/0-% *&' &&-(&%+ *& C:'/*%-9 +)& & *&(+/@/% '/ *->&&%& -(<&%& <&+(=-0/ )& +*)0&% '/ +%*/ &/0-+%/-/ &% *--%/ >&0)&%0-/ /*&( 0+% &/ &&-&%0-/ '+</&(+ -')/ '/ +%*/ (&0%-0/9 '/ )&+-0-% *& +%*/9 '+ %+*+ ,/''&. E& +&0+ ,/ &%0/(-%/*+ / &0&/ */ / 0+%+0& 0+%0&+ 8-0+ *& '/ >+(/ *& +/0-% *&' +%-*+ / /,= *& '/ (/&-/. C)' & ) :)&''/ *-<-/' +*@/(+ *&0-9 /' ,-/?/ + )% (&*-+ (/&-/'. A /- *& '/ 0&/0-% *& )% +%+0-+9 +*&(+ *&&(-%/ '/ -(<&%& *& C:'/*%// 0/*/ (+(&%+ &% )& '/ >&0)&%0-/ /)(&%& 0+% &''/ '/ ,-8/0-% *&' 8-0/8+%/+ *& +*-+9 /' + /&%/ +8&)&/ &% '/ '/0/ (&'-0/ *-8)?&% +8& &/9 /+%& /')0-%/%& 0/(8-/%& )& %+ &(-/% *&(+/ '/ %/)/'&;/ *& &)8/0-% *& +%*/ *& +%-*+ /' -<)/' )& '/ *->&&%& +%*/. E %&0&/-+ /(8-=% &/'-;/ '/ *&(+/0-% &&-(&%/' *&' >)%0-+%/(-&%+ *& '/ '/0/ *& C:'/*%- / )& &% =' & +8&,/% >-<)/ () ,-+/ &+ *->@0-'& *& &'-0/9 )& %+ & 0+&+%*&% +/'(&%& 0+% '+ /+%& &*-0:+ &-0/(&%&9 '+ 0)/'& & &0+<&% &% &' '-8+ T:& P:-0 +> M)-0/' I%)(&%9 *& F'&0:& R+-%<. D-0:/ *-0&/%0-/ )&*&% *&8&& / )& '/ <&+(&@/ %+ & '/ -*&/'H '/ '/0/ %+ & )%/ (&(8/%/ -*&/'9 '+ 8+*& &% *+8'/*+9 &0.
%. OBJETIVOS %.1 OBJETIVO GENERAL R&0&/ &% &' '/8+/+-+ '/ >-<)/ *& C:'/*%- 0+% )% +%+0-+ &' 0)/' %+ &(-/ '/ ,-)/'-;/0-% *& '+ %+*+ +-+ *& ,-8/0-% *& )%/ '/0/ 0)/*/*/ & +8&,/% '+ /+%& '@%&/ %+*/'& )& & >+(/% &% '/ (-(/9 0+&+%*-=%*+& 0/*/ /% 0+% )% %+*+ +-+ + >&0)&%0-/ +-/ *& ,-8/0-% *& '/ '/0/.
%.2 OBJETIVOS ES!ECIFICOS •
D&(+/ &' &&-(&%+ *& C:'/*%- &'-0/ ) >)%0-+%/(-&%+.
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P&(-- &' &)*-+ *& +%*/ &/0-+%/-/ &% *+ *-(&%-+%&.
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V-)/'-;/ '/ +/0-% *& '/ +%*/ +%+/ (&0%-0/ <&%&/*/ + &' +%-*+ / /,= *& '/ (/&-/
&. METODOLOGÍ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
'. IMÁ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S& *&%+(-%/% ()"#*+* -* C/-+( / '+ /+%& >+(/*+ + )%/ )/%0-/ </%)'/ +8& )%/ )&>-0-& '/%/ ,-8/%*+ &% )% (+*+ +-+. A' +/& +%*/ (&0%-0/ + )% +8?&+ &&%*-*+9 '+ :/0&% &% +*/ *-&00-+%&. D&&%*-&%*+ *& '/ '+%<-)*& 0//0&@-0/ *&' 0)&+9 '/ 0+%*-0-+%& *& 0+%+%+ )& && -(+%& / '/ +%*/ )&*&% -%*)0-
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ONDAS MECANICAS
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ONDAS ESTACIONARIAS L/ 3+- *4(3+( +% +%*/ +*)0-*/ &% 5+ )*-(3 /()(-39 0+(+9 + &?&('+9 )%/ 0)&*/ &'-0/ %+ () '/ >-?/ &% /' (&%+ )%+ *& ) *+ &&(+. P// <&%&/ &% *-0:/ 0)&*/ )%/ +%*/ &/0-+%/-/9 & )&*& // + )% &&(+ / )%/ /&* :/0& ,-8/ /' ++ 0+% )%/ &)&/ /('-)*. S& +8-&%&% )'+ /%,&/'& )& ,-/?/% :// '/ /&*9 *+%*& & &>'&?/% ,)&',&%. L/ 0)&*/ & &0+-*/ + *+ +%*/ *& &%-*+ +)&+ & +*)0&% -%&>&&%0-/ )&9 &% -%0--+9 */% ') / )%/ +0-'/0-+%& 8//%& *&+*&%/*/. A)(&%/%*+ '/ >&0)&%0-/ 0+% '/ )& & /<-/ &' &&(+ *& '/ 0)&*/ & )&*& 0+%&<)- )& '/ +0-'/0-+%& /*)-&/% &' &>-' (+/*+ + '/ >-<)/ /*?)%/. C+&+%*& / )%/ +%*/ &% '/ )& /)(&%/ &%-8'&(&%& '/ /('-)* -&%& )% ,-&%& >-?+ &% &' 0&%+ *+ %+*+ /(8-=% >-?+ &% '+ &&(+. E/ +%*/ & ''/(/ &/0-+%/-/ +)&9 / *->&&%0-/ *&' &+ *& +%*/9 &% '/ )& & /&0-/ )% /,/%0& *& '/ 0&/ '+ ,/''&9 %+ /&0& (+,&&. S- & >-?/% '+ *+ &&(+ *& '/ 0)&*/ & &-/ /%,&/'(&%& *& )%+9 *+9 & )%+ & )&*&% <&%&/ &% '/ 0)&*/ )%/ &0)&%0-/ *& +%*/ &/0-+%/-/ 0+% )% %(&+ 0&0-&%& *& %+*+ ,-&%&9 0+(+ '/ -%*-0/*/ &% '/ >-<)/ /*?)%/.
F-<)/ 39 E)&(/ *& +%*/ &/0-+%/-/.
ELEMENTOS DE UNA ONDA
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