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

= 3.0 mm, k = 60 cm

−1

, and ω = 2π/T = 2π/0.20 s = 10π s

−1

. Thu s

z(y, t) = (3.0 mm) sin



60 cm

−1



y

−



10π s

−1



t



.

(b) The maximum transverse speed is

u

m

= ωz

m

= (2π/0.20 s)(3.0 mm) = 94 mm/s .