Chapter K  Problems
Blinn College  Physics 2425  Terry Honan
Problem K.1
Consider a pulse that in SI units has the shape
u
=
f
H
x
L
=
8
x
2
+
4
.
Write this as a function
u
H
x
,
t
L
that describes this pulse moving in the positive
x
direction with a speed of 3
m
ê
s
.
Solution to K.1
A pulse of shape
u
=
f
H
x
L
moving in the positive xdirection with speed
v
takes the form:
u
=
f
H
x

v t
L
. Using this form of
f
H
x
L
with
v
=
3
m
ê
s
gives:
f
H
x
L
=
8
x
2
+
4
ï
u
=
8
H
x

3
t
L
2
+
4
.
Problem K.2
What are the speed and direction of a pulse on a string that (in SI units) has the form:
y
H
x
,
t
L
=
0.04
e

J
x
+
0.03
t
0.06
N
2
.
Solution to K.2
A wave of the form:
y
H
x
,
t
L
=
f
H
x
°
v t
L
represents a pulse of shape
y
=
f
H
x
L
moving in the
±
x
direction with speed
v
. Here we have
y
H
x
,
t
L
=
0.04
e

H
x
ê
0.06
L
2
with
v
=
0.03
m
ê
s
moving in the negative
x
direction.
Problem K.3
A sinusoidal pulse on a string has the mathematical form
y
H
x
,
t
L
=
H
0.80 m
L
sin
B
2
p
10
H
x

4
t
LF
. Plot the
y
vs.
x
graph at
t
=
0 s. By the
time
t
=
0.6 s how much has the pulse shifted. On the same graph plot
y
vs.
x
at
t
=
0.6 s.
Solution to K.3
After
t
=
0.6 s the graph has shifted by
v t
=
4
μ
0.6
=
2.4 m.
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10
15
20
x
H
m
L

0.75

0.5

0.25
0.25
0.5
0.75
y
H
m
L
Problem K.4
A string with a linear density of
m =
4
μ
10

3
kg
ê
m is given a tension of 360 N. What is the speed of waves on this string?
Solution to K.4
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 Spring '09
 Physics, Simple Harmonic Motion, Frequency, Wavenumber, linear density

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