72.
(a) The wave number for each wave is
k
=25
.
1
/
m, which means
λ
=2
π/k
= 250 mm. The angular
frequency is
ω
= 440
/
s; therefore, the period is
T
=2
π/ω
=14
.
3 ms. We plot the superposition of
the two waves
y
=
y
1
+
y
2
overthet
imeinterva
l0
≤
t
≤
15 ms. The Frst two graphs below show
the oscillatory behavior at
x
= 0 (the graph on the left) and at
x
=
λ/
8
≈
31 mm. The time unit
is understood to be the millisecond and vertical axis (
y
) is in millimeters.
–1
0
1
5
10
15
t
–2
0
2
5
10
15
t
The following three graphs show the oscillation at
x
=
λ/
4
≈
63 mm (graph on the left), at
x
=3
λ/
8
≈
94 mm (middle graph), and at
x
=
λ/
2
≈
125 mm.
–4
–2
0
2
4
5
10
15
t
–2
0
2
5
10
15
t
–1
0
1
5
10
15
t
(b) If we think of wave
y
1
as being made of two smaller waves going in the same direction, a wave
y
1
a
of amplitude 1
.
50 mm (the same as
y
2
)andawave
y
1
b
of amplitude 1
.
00 mm. It is made clear
in
§
1711 that two equalmagnitude oppositelymoving waves form a standing wave pattern. Thus,
waves
y
1
a
and
y
2
form a standing wave, which leaves
y
1
b
as the remaining traveling wave. Since
the argument of
y
1
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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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