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y
1
b
as the remaining traveling wave. Since the argument of
y
1
b
involves the subtraction
kx
–
ω
t
, then
y
1
b
travels in the +
x
direction.
(c) If
y
2
(which travels in the –
x
direction, which for simplicity will be called “leftward”)
had the larger amplitude, then the system would consist of a standing wave plus a
leftward moving wave. A simple way to obtain such a situation would be to interchange
the amplitudes of the given waves.
(d) Examining carefully the vertical axes, the graphs above certainly suggest that the
largest amplitude of oscillation is
y
max
= 4.0 mm and occurs at
x
=
λ
/4 = 62.6 mm.
(e) The smallest amplitude of oscillation is
y
min
= 1.0 mm and occurs at
x
= 0 and at
x
=
λ
/2 = 125 mm.
(f) The largest amplitude can be related to the amplitudes of
y
1
and
y
2
in a simple way:
y
max
=
y
1
m
+
y
2
m
, where
y
1
m
= 2.5 mm and
y
2
m
= 1.5 mm are the amplitudes of the original
traveling waves.
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This note was uploaded on 04/16/2011 for the course PHYSICS 191262 taught by Professor Najafzadeh during the Spring '09 term at The Petroleum Institute.
 Spring '09
 NAJAFZADEH
 mechanics

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