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69. (a) We take the form of the displacement to be
y
(
x, t
) =
y
m
sin(
kx
–
ω
t
). The speed of
a point on the cord is
u
(
x, t
) =
∂
y
/
∂
t
= –
y
m
cos(
kx
–
t
),
and its maximum value is
u
m
=
y
m
. The wave speed, on the other hand, is given by
v
=
λ
/
T
=
/
k
. The ratio is
2
.
/
mm
m
m
uy
y
ky
vk
π
==
=
λ
(b) The ratio of the speeds depends only on the ratio of the amplitude to the wavelength.
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 Spring '09
 NAJAFZADEH
 mechanics

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