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47. (a) The angular frequency is
ω
=8
.
0
π/
2=4
.
0
π
rad
/
s, so the frequency is
f
=
ω/
2
π
=(4
.
0
π
rad
/
s)
/
2
π
=
2
.
0Hz.
(b) The angular wave number is
k
=2
.
0
π/
2=1
.
0
π
m
−
1
, so the wavelength is
λ
=2
π/k
=2
π/
(1
.
0
π
m
−
1
)=
2
.
0m.
(c) The wave speed is
v
=
λf
=(2
.
0 m)(2
.
0Hz)=4
.
0m
/
s
.
(d) We need to add two cosine functions. First convert them to sine functions using cos
α
= sin(
α
+
π/
2),
then apply Eq. 42. The steps are as follows:
cos
α
+cos
β
=
sin
³
α
+
π
2
´
+ sin
³
β
+
π
2
´
= 2 sin
µ
α
+
β
+
π
2
¶
cos
µ
α
−
β
2
¶
=2
c
o
s
µ
α
+
β
2
¶
cos
µ
α
−
β
2
¶
Letting
α
=
kx
and
β
=
ωt
, we ±nd
y
m
cos(
kx
+
ωt
)+
y
m
cos(
kx
−
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.
 Fall '08
 SPRUNGER
 Physics

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