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18.
(a) The general expression for
y
(
x, t
)forthewaveis
y
(
x, t
)=
y
m
sin(
kx
−
ωt
), which, at
x
=10cm
,
becomes
y
(
x
=10cm
,t
)=
y
m
sin[
k
(10 cm
−
ωt
)]. Comparing this with the expression given, we
Fnd
ω
=4
.
0rad
/
s, or
f
=
ω/
2
π
=0
.
64 Hz
.
(b) Since
k
(10 cm) = 1
.
0, the wave number is
k
=0
.
10
/
cm. Consequently, the wavelength is
λ
=
2
π/k
=63cm
.
(c) Substituting the values of
k
and
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 Fall '08
 SPRUNGER
 Physics

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