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 .