Physics 21
Fall, 2004
Solution to HW19
Problem 1
A wave on a string travels at 5 m/s toward
the right (labeled the positive
x
direction). The transverse
displacement of the string at a point arbitrarily labeled
x
= 0
is observed to be
y
0
(
t
) = 0
.
03
e
−
0
.
6
t
cos(50
t
)
,
where
t
is in seconds and
y
is in meters.
(a) What is the
mathematical expression for the traveling wave on the string
as a function of
x
and
t
?
(b) Answer part (a) for a wave
moving toward the left rather than toward the right.
Replace
t
by
t
±
x/v
, using the upper (lower) sign for
propagation to the left (right):
y
0
(
x, t
) = 0
.
03 exp
−
0
.
6
t
±
x
v
cos 50
t
±
x
v
For
v
= 5 m/s,
y
0
(
x, t
) = 0
.
03 exp [
−
0
.
6
t
∓
0
.
12
x
] cos [50
t
±
10
x
]
.
Problem 2
What is the frequency of yellow light with a
wavelength of 5
.
9
×
10
−
7
m in empty space?
λf
=
c
⇒
f
=
c/λ
=
3
×
10
8
5
.
9
×
10
−
7
= 5
.
1
×
10
14
Hz
Problem 3
The mathematical expression for a traveling
wave on a string is given by
y
(
x, t
) = 0
.
03 sin(40
πt
+ 8
πx
)
where
x
and
y
are in meters,
t
is in seconds, and
x
≥
0. (a)
In what direction does the wave propagate?
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 Fall '07
 Hickman
 Physics, Wavelength, m/s, 1.0 M, 1.8 m, 0.25 m

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