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SOLVING PROBLEM 9
April 7, 2010
(like 13.18): A sinusoidal traveling wave is approaching the origin
traveling left (from the +
x
side) on a taught piece of string fixed at the
origin (
x
=0). The wave velocity is 10 m/s and the wavelength is 1 m. When
the wave is isolated from any reflections (i.e. far from the origin) its
amplitude is 0.1 m. When the wave is bouncing off the fixed point at the
origin, what is the amplitude of the wave motion of the part of the string
that is one quarter wavelength from the origin?
a)
0.2 m;
b)
2 m;
c)
20
m;
d)
0.02
m;
e)
0.002 m.
What do you know?
If the string is fixed, the amplitude is
zero there. Thus when the wave is reflecting off the fixed
point it will be a sum of the original wave going left
)
sin(
)
,
(
t
kx
A
t
x
y
plus a wave going right with the same amplitude but
possibly a different phase:
)
sin(
)
,
(
'
t
kx
A
t
x
y
.
At the origin the sum is
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