15.10:
a) The relevant expressions are
)
cos(
)
,
(
t
ω
kx
A
t
x
y

=
)
(
sin
ωt
kx
ωA
t
y
v
y

=
∂
∂
=
).
(
cos
2
2
2
kx
ωt
A
ω
t
v
t
y
a
y
y


=
∂
∂
=
∂
∂
=
b) (Take
A
,
k
and
ω
to be positive. At
,
0
=
t
x
the wave is represented by (19.7(a)); point
(i) in the problem corresponds to the origin, and points (ii)(vii) correspond to the points
in the figure labeled 17.) (i)
,
)
0
cos(
ωA
ωA
v
y
=
=
and the particle is moving upward (in
the positive
y
direction).
,
0
)
0
sin(
2
=

=
A
ω
a
y
and the particle is instantaneously not
accelerating. (ii)
,
2
)
4
cos(
ωA
π
ωA
v
y
=

=
and the particle is moving up.
,
2
)
4
sin(
2
2
A
ω
π
A
ω
a
y
=


=
and the particle is speeding up.
(iii)
,
0
)
2
cos(
=

=
π
ωA
v
y
and the particle is instantaneously at rest.
,
)
2
sin(
2
2
A
ω
π
A
ω
a
y
=


=
and the particle is speeding up.
(iv)
,
2
)
4
3
cos(
ωA
π
ωA
v
y

=

=
and the particle is moving down.
,
2
)
4
3
sin(
2
2
A
ω
π
A
ω
a
y
=


=
and the particle is slowing down (
y
v
is becoming less
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.