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Chapter 17 - 17.64

64. (a) Let the displacements of the wave at ( y, t )be z ( y, t ). Then z ( y, t )= z m sin( ky

−

ωt ), where

z m =3 . 0mm, k =60cm − 1 ,and ω =2 π/T =2 π/ 0 . 20s = 10 π s − 1 .Thus

z ( y, t )=(3 . 0mm)sin 60cm − 1 y

− 10 π s − 1 t .

(b) The maximum transverse speed is

u m = ωz m =(2 π/ 0 . 20s)(3 . 0mm)=94mm / s .