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(d) The angular frequency is
ω
= 2
π
/
T
=
π
/5 = 0.63 rad/s.
(e) As found in part (a), the phase is
φ
π
=
.
(f) The sign is minus since the wave is traveling in the +
x
direction.
(g) Since the frequency is
f
= 1/
T
= 0.10 s, the speed of the wave is
v
=
f
λ
= 2.0 cm/s.
(h) From the results above, the wave may be expressed as
( , )
4.0sin
4.0sin
10
5
10
5
x
tx
t
yxt
ππ
§·
§
·
=−
+
=
−
−
¨¸
¨
¸
©¹
©
¹
.
Taking the derivative of
y
with respect to
t
, we find
(,)
4
.
0
c
o
s
10
5
y
xt
uxt
tt
∂π
§· §
·
==
−
¨¸ ¨
¸
∂
©¹ ©
¹
which yields
u
(0,5.0) = –2.5 cm/s.
13. From Eq. 1610, a general expression for a sinusoidal wave traveling along the +
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 Spring '08
 Any
 Physics

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