Informe N3. Cuerdas Vibrantes

8/18/2019 Informe N3. Cuerdas Vibrantes

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INDICE

RESUMEN 2

INTRODUCCION 3

FUNDAMENTO TEÓRICO 4

I. ONDAS MECANICAS 4

II. ONDAS TRANSVERSALES 4

III. ONDAS ESTACIONARIAS……………………………………………………………………5

OBJETIVOS 6

METODOLOGÍA 6

CÁLCULOS Y RESULTADOS 9

DISCUSIÓN DE RESULTADOS 12

OBSERVACIONES 13

CONCLUSIONES 14

BIBLIOGRAFÍA 15

APNDICES 16

I. APÉNDICE 1: DIAGRAMA DE EQUIPO 16

II. APÉNDICE 2: DATOS DE LABORATORIO 17

III. APÉNDICE 3: MUESTRA DE CALCULOS 18

IV. APENDICE 4: DATOS CALCULAROS……………………………………………………1

V. APENDICE 5: ANALISIS DE ERRORES……………………………………………..………….….1

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RESUMEN

E! "#$% "&'"()"!*)% #" $)"!" *+,+ +-"$)/+ 0"$"(,)!%( %# ("%*)+!"# "&)#$"!$"# "!$(" %

"(% #+-(" % *"(0% *+! % ("*"!*)% /"+*)0%0. P%(% "+ ("*+"(",+# +# 0%$+#

!"*"#%()+# '%(% '+0"( %*"( +# *9*+# ("#'"*$)/+#.

S" $)) %# '()!*)'%"# (,%# 0" !% +!0%; *+,+ '%(% %%# % /"+*)0%0 V "!

!*)! 0" % "(% + $"!#)!

V =√ F

µ

T%,-)

"((+( >" !+# )!0)*%(=% *%! "%!+ "#$% !"#$(+# 0%$+# 0" % ("%)0%0.

E#$% "&'"()"!*)% #" "/ % *%-+ " 6 0" M%+ 0" 2?15 "! " L%-+(%$+()+ 0" =#)*%; "! %

%*$%0 0" C)"!*)%# 0" % UNI.

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INTRODUCCION

E '("#"!$" )!+(," 0" =#)*% "/% '+( $=$+ *"(0%# /)-(%!$"#; "! " *% $(%$%(",+# "

$",% 0" +!0%# "#$%*)+!%()%#

D(%!$" "#$% "&'"()"!*)% #" $))%(% " #)#$",% '+"%@/)-(%0+(; % % *"(0% #" "

#+,"$"(9 % !% $"!#)! 0)#$)!$% *%0% /"; % >" %(",+# /%()%0%# *+,-)!%*)+!"# 0" ,%#%#;

*+! %>"+# 0%$+# *%*%0+# '+0(",+# '("0"*)( '+( "",'+ % /"+*)0%0 0" % *"(0% %

*)"($% $"!#)!.

E#$" )!+(," "# #,%,"!$" ),'+($%!$" '+(>" "# !"#$(% /)0% *+$)0)%!% #)",'("

$"!",+# *+!$%*$+ *+! !% +!0%; #+-("$+0+ "! " %!9)#)# 0" % ),'+($%!*)% 0" %# *"(0%# "!

+# )!#$(,"!$+# ,#)*%"#; " "*+; "$*. E#$" )!+(," !+# %0%(% % *+,'("!0"( ,"+( #

!%$(%"%.

A )!%)%( "#$" )!+(," #" "#'"(% >" " "*$+(; %#),)#,+ " ("%)%0+( 0" "#$" )!+(,";

#" 0< *"!$% >" % =#)*% "# !% *)"!*)% "&'"(),"!$% >" !+# %0% % *+,'("!0"(

"!,"!+# *+$)0)%!+#; >" % (%! ,%+(=% '%#% '+( %$+.

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UNDAMENTO TEORICO

Ondas Mecánicas

U!% +!0% ,"*9!)*% "# !% '"($(-%*)! >" +*((" "! ! ,"0)+; 0+!0" %# '%($=*%#

0" 0)*+ ,"0)+ +#*)%! 0" "#$% +(,% $(%!#,)$"! "!"(=% *%!$)0%0 0" ,+/),)"!$+.

D" %*"(0+ % % 0)("**)! "! % >" +#*)%! %# '%($=*%# 0" ,"0)+ ("#'"*$+ % %

/"+*)0%0 0" % +!0%; #" *%#))*%! "! +!0%# +!)$0)!%"# +!0%# $(%!#/"(#%"#.

Ondas Longitudinales

S+! %>"%# "! %# >" %# '%($=*%# 0" ,"0)+ +#*)%! "! % ,)#,% 0)("**)! 0+!0"

#" 0)()" % +!0%.

Ondas Transversales

S+! +!0%# "! %# >" %# '%($=*%# 0" ,"0)+ +#*)%! 0" ,%!"(% '"('"!0)*%( % %

0)("**)! "! >" #" 0)()" % +!0%.

E! !% *"(0% $"!#% #" '"0" '(+'%%( !% +!0% $(%!#/"(#% 0" % #))"!$" +(,%:

&

6

L+!7)$30 0" O!0%

A,'1)$30

&

6

o Velocidad de Onda ( ):ѵ E# % (%')0" *+! >" #" '(+'%% % +!0%.

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o Longitud de Onda (λ): E# % +!)$0 >" ("*+((" % +!0% 0(%!$" # '"()+0+.

o Periodo (T): E# " $)",'+ "! >" ! '!$+ $%(0% "! ("("#%( % ! ,)#,+ "#$%0+.

o Frecuencia (f): E# % )!/"(#% 0" '"()+0+. S" '"0" *%*%( *+,+ " !,"(+ 0"

+#*)%*)+!"# 0" +*(("! '+( !)0%0 0" $)",'+.

o Tensión (F): E# % "(% 0" $"!#)! >" % "! % *"(0% $"!#%.

o Densidad Lineal (μ): E# % ,%#% '+( !)0%0 0" +!)$0 0" % *"(0%.

L% '+#)*)! 0" !% '%($=*% "! *%>)"( '!$+ #" *%*% *+,+:

y= ASen(wt ± kx+∅)

U#%!0+ %# 0")!)*)+!"# #" $)"!" >" v= λf

A0",9#; % /"+*)0%0 0" '(+'%%*)! 0" % +!0% $%,-)

#))"!$" ,%!"(%:

v=√ F

μ

R"",'%%!0+ "#$% "&'("#)! "! % %!$"()+(; +-$"!",+#:

f =1

λ √ F

μ

Interferencia y Principio de Superposición de Ondas

E '()!*)')+ 0" #'"('+#)*)! 0" +!0%# "#$%-"*" >" % ,%!)$0 0" 0"#'%%,)"!$+

"! % +!0% "! *%>)"( '!$+ 0" ,"0)+ "# )% % % #,% 0" +# 0"#'%%,)"!$+# "!

"#" ,)#,+ '!$+ 0" $+0%# %# +!0%# '("#"!$"#.

Ondas Estacionarias

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L%# +!0%# "#$%*)+!%()%# #" '(+0*"! 0"-)0+ % % )!$"("("!*)% 0" 0+# +!0%# >" /)%%!

"! ! ,)#,+ ,"0)+ *+! % ,)#,% ("*"!*)% +!)$0 0" +!0%. D)*% )!$"("("!*)% "#

+*%#)+!%0% '+( !% /)-(%*)! "! !% *"(0% $"!#% $)"!" " #))"!$" '"() 0" +!0%

OBETIVOS

• E#$0)%( "&'"(),"!$%,"!$" % ("%*)! "!$(" % ("*"!*)%; $"!#)!; 0"!#)0%0

)!"% +!)$0 0" +!0% 0" !% +!0% "#$%*)+!%()% $"!#%.• D"$"(,)!%( (9)*%,"!$" +# '!$+# 0+!0" #" "!*"!$(% ,%+( "!"(=% '+$"!*)%

*)!


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D)%(%,%:

7

1°.

2°.

3°.

Hacemos


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9/19

RESULTADOS

1 P%(% %*"( % (9)*% 2

/# ; $))%(",+# +# 0%$+# 0" %-+(%$+()+ -)*%0+ "! "

A'


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2 P"() 0" !% *"(0% *+! % '+#)*)! ,%+( E!"()% *)!"$)*% % '+#)*)! ,%+( E!"()%P+$"!*)%.

M%+( "!"(=% *)!" '%(% !%

+!0% /)%"(% "! !% +!)$0 0" +!0% % "! $+0+ ,+,"!$+ '!$+# *+! /"+*)0%0 ,9&),%

'!$+# "! ("'+#+; $+0%# %# '+#)-))0%0"# )!$"(,"0)%#. E! !% +!0% "#$%*)+!%()% $+0+# +#

'!$+# +#*)%! % !=#+!+ 0" +(,% >" "! ! )!#$%!$" $+0+# $)"!"! % /"+*)0%0 ,9&),% J %

"!"(=% *)!


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3 P%(% %%( % (9)*% V2 /# $))%(",+# +# 0%$+# +-$"!)0+# "! " %-+(%$+()+

D%$+#:

% V2

&.775'71

&.&&2&'722

&.871128

&.&&23544

1.153656

&.&&3117''

&.16&884

&.&&&43482

&.1'8162

&.&&&53557

&.1'8162

&.&&&53557

G(%)*%:

f()* + 37&)

,- + 1

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DISCUSION DE RESULTADOS

E! "#$% "&'"()"!*)% +-$/),+# 2 (%)*%#. E! % '(),"(% *%!0+ #" ("%*)+!% % "(% *+! "

*%0(%0+ 0" % ("*"!*)%; #" +-$)"!" !% (9)*% >" !+ #" '("0"*)(; "# 0"*)( >" !+ #" '"0"

+-$"!"( !% "*%*)! 0" *%>)"( $)'+. P"(+; '+( >" +*((" "#$+K E#$+ #" 0"-" % >" *%!0+

#" >)"(" %%( "#% ("%*)!; % +!)$0 0" +!0% #" "!*"!$(% )!/+*(%0% "! 0)*% ("%*)!;

% +!)$0 0" +!0% !+ "# *+!#$%!$"; '+( + >" % ("%*)! /%()% *+!+(," *%,-)%,+# 0"

0)#$%!*)% 0" % *"(0%.

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E! % #"!0% (%)*% #" +-$/+

!% '"!0)"!$"; >" ("'("#"!$% %

'"!0)"!$"; "! '(),"( %( !+#+$(+#

)!/"($),+# % $%-%; '%(% >" %

'"!0)"!$" #"% ! "!$"(+ !+ !

!,"(+ 0"*),% '"()0)*+ '(+.

P"(+ 0" !% ,%!"(% +$(% #"

+-$)"!" ! ? 0" "((+(. L%

'"!0)"!$" ("'("#"!$% % 0"!#)0%0

)!"%; % *% "# *+!#$%!$" 0(%!$"

$+0% % "&'"()"!*)% + #")(9 #)"!0+ '+(>" % *"(0% "# !)+(,"; % 0)"("!*)% *+! %

%!$"()+(; "! % ("%*)! !+ )!$"(/)"!"! 0%$+# /%()%-"# #)!+ *+!#$%!$"#; "# '+( "+ >" #" '"0"

%%( !% *+!#$%!$".

OBSERVACIONES

• S" +-#"(/% >" % ("*"!*)% % /"+*)0%0 %,"!$%! *+!+(," %,"!$% % "(%.

• S" +-#"(/% >" % (9)*% 0" V2 /"(## ; "# !% !*)! )!"%.

• S" +-#"(/% >" '%(% !% ,)#,% ! 0)"("!$" 0" 2 % +!)$0 0" +!0% /% %,"!$%( #)

%,"!$% % +!)$0 0" % *"(0%.

• S" +-#"(/% >" '%(% ! !2 % +!)$0 0" +!0% "# % ,)#,% >" % +!)$0 0" %

*"(0%.

• S" +-#"(/% >" #) " /)-(%0+( !+ #" )% -)"! "! % ,"#%; %# +!0%# "! /" 0" #"(

$(%!#/"(#%"# #" +(,%! "! +!0%# +!)$0)!%"#.

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• S" +-#"(/% >" % +!0% "#$%*)+!%()% #++ #" +(,% 0"#0" " "&$(",+ 0" % *"(0% #"$%

% /)-(%0+( %#$% " '!$+ 0" *+!$%*$+ 0" % *"(0% *+! % '+"%.

• S" +-#"(/% >" '%(% !% ,)#,% "(% " ! %,"!$% *+!+(," #" %,"!$% % +!)$0

L.

• L% +!)$0 0" % ,"#% 0" %'++ '%(% %!+# *%#+# " )!#)*)"!$".

• L% ,"0)*)! 0" %# +!)$0"# 0" +# /)"!$("# !+ "#$9! '("*)#% $))%!0+ ("%; % >"

#" )!$"()"(" # /)-(%*)!.

• P%(% " *%*+ 0" % "!"(=% *)!" +$(+# *9*+# ,9#.

• P%(% %%( " '"#+ $+$% >" ""(*" $"!#)! "! % *"(0% 0"-",+# *+!#)0"(%( $%,-)" $"!"( ,*+

*)0%0+ % >" #) >"(",+# $"!"( !+# ("#$%0+# ,9# '("*)#+# $"!",+# >" /%()%(

"!$%,"!$" '">"%# +!)$0"# '%(% "!*+!$(%( % /"(0%0"(% J% ,9# *"(*%!% +(,% 0"

+#*)%*)! 0" % *"(0% $"!#%.

CONCLUSIONES

A!>" +-$/),+# *+,+ ("#$%0+ ! '+(*"!$%" 0" "((+( 0" ?; !+$%,+# >" #)

%*",+# (""("!*)% % % '%($" 0" % "*%*)! +-$"!)0% 0" % (9)*%; ",+# 0"

*+!#)0"(%( %>"+# %*$+("# *+! ,$)'+# % %# ,)" !"#$(+ "&'"(),"!$+ ("%)%0+ $)"!0" % %

"*%*)! )0"% 0" !% +!0% "#$%*)+!%()%.• L%# +!0%# "#$%*)+!%()%# #" '(+0*"! '%(% 0"$"(,)!%0%# *+!0)*)+!"# 0" "(%;

*%(%*$"(=#$)*%# 0" % *"(0% ("*"!*)% 0" +#*)%*)! 0" /)-(%0+( "


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• E !,"(+ 0" /)"!$("# 0"'"!0" 0" % "(% %')*%0% % +!)$0 0" % *"(0%.• L%# ("%*)+!"# 0" "!"(=%# ,9&),%# $%!$+ 0" *)!" "! " #" " %')>" % % *"(0%.• T%,-)" "! ("%)0%0 #) %,"!$% % ("*"!*)% % /"+*)0%0 *+!+(,"

%,"!$% % $"!#)! + % "(% %')*%0%.

BIBLIOGRAIA

• SERAF; R%,+!0 A. EETT; +! . J2??2 =#)*% I T"&$+ -%#%0+ "! *%*+; 3

E0. $+,+ I E0)$+()% T+,#+!.• TOMAS; A. MOORE. J2??3 =#)*% #")# I0"%# !0%,"!$%"#. MCGRA ILL.• U!)/"(#)$ L%-+(%$+( E&'"(),"!$# P#)*#. V+,"! 1. E0)*)! 45.

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Il"s!racin 4/ ,ela milime!rada

Il"s!racin 1/ 0"a!ro masas diferen!es

Il"s!racin 2/ balana elec!rnica

Il"s!racin 5/ $olea incor$orada a $rensa

Il"s!racin 3/ vibrador

APENDICES

APENDICE 1. DIAGRAMA DE EQUIPO

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Il"s!racin 6/ balde $e#"eo

Il"s!racin 7/ 0"erda

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APENDICE 3 MUESTRA DE CALCULO

1 P%(% %%( % '"!0)"!$" 0" % (9)*% 2; $))%(",+# +# 0%$+# 0" %-+(%$+()+.

% V2

&.775'7

1

&.&&2&'7

22&.87112

8&.&&2354

41.15365

6&.&&3117

''&.16&88

4&.&&&434

82&.1'816

2&.&&&535

57&.1'816

2&.&&&535

57

R"%)%,+# " %#$" 0" '!$+# *+! " +-"$)/+ 0" !% ("*$%:

∑¿1

n

I n=B .n+ A .∑¿ 1

n

Ln2

∑¿1

n

I n Ln2=B .∑

¿1

n

Ln2+ A .∑

¿ 1

n

Ln4

R"#+/)"!0+ " #)#$",% 0" "*%*)+!"# )!"%"# '%(% "#$" %#$"; +-$"!",+#: 1?@6

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A=370 B=−3 x 1?@6

APENDICE 4 DATOS DE LABORATORIO

1 L% '"!0)"!$" 0" % ("*$% +-$"!)0% "# 37?; >" ("'("#"!$% % % 0"!#)0%0 )!"%

APENDICE 5 ANALISIS DE ERROR

1 37? D"!#)0%0 )!"% $"+()*%37? D"!#)0%0 )!"% "&'"(),"!$%

E '+(*"!$%" 0" "((+( "# ?

1'

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