solutionshw5 - ! # ! ! !! ! $ ! % " ! %...

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Unformatted text preview: ! # ! ! !! ! $ ! % " ! % &'(" ) *" ! , ! ! " ! ! ! , "+ ! ! !. % % % ! ! " % / ! ! ! ! % ! !% 0 % ! "# " ! ! ! " % !! % ! ! !! % 1 2' % % 3 & 0 0 0 &3 &3" & 3 & &3 3 1 4 % !! " !! 5 % 67 ∆x = 9.00 + 4.00 − 3.00 = 13 − 3.00 = 0.606 m λ= v 3 43 m s = = 1.14 m f 300 Hz ∆x 0.606 = = 0.530 of a wave λ 1.14 ∆φ = 2π ( 0.530) = 3.33 rad # ! % 6%7 4 ∆x !! 5 % ! 8 " ! " ∆x ∆x = 0.500 = f λ v v 343 f= = = 283 Hz 2 ∆x 2 ( 0.606) 1 % 67 9 : ; :& 9 '"' 6 ;%7>& 9 0>& 9 '"'? * 60>&7 9 ' 0 9 6& ; 7 6%7 ! 60>&7 < ; %= 6 $%7>& 9 $ ' 6'7 , ! & 0>& 9 6& ; 7 ! 0 6 ' 79 : 0609'" 7 9 '"'? 0 % 6"&7 9 '"'&2 1 ∂y ∂x 2 2 % ) y = 2 A0 sin kx cos ω t ∂2 y ∂t 2 = − 2 A0 ω 2 sin kx cos ω t = −2 A0 k 2 sin kx cos ω t % 8 1 − 2 A0 k 2 sin kx cos ω t = 2 − 2 A0 ω 2 sin kx cos ω t v ( ) ω k ! v= 1 @ % &' ! 9 9 )" !! ! 8 &@ ' '"'' '"'' ) 0 2" > A& 9 ?2"& * # 4 ! B ' "B , 1 % &) '* '"' B'"B 4 ! 8 ! ! ! ! &@ B'"B "& "2 , &' '''' C 8 &'''' ??2 "2 ??2 0 "2 22)B , 1 % ? D @ 4 @ ! &@ ?? '")? & &) ") &) ") @ ?? &) ") ") &) ") 1% # ' $8 3*3*3 ! ! L = 2dAA = λ " L= % v 5 100 m s = = 1.16 m 4 400 Hz f 1 67 % & % " 6%7 !8 % % 67 4 f2 f1 f= 521 Hz or 525 Hz ! " -! 8 526 Hz " v = λ Tµ 2L ! 8 " & & , , ! = 1T 2L µ 2 = T2 T1 2 f 523 Hz T2 = 2 T1 = T = 0.989T1 " 526 Hz 1 f1 ! % ! = T1 − T2 T1 = 1 − 0.989 = 0.011 4 = 1.14% " % reduced by 1.14% " ...
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