homework 33 – PAPAGEORGE, MATT – Due: Apr 19 2008, 4:00 am
1
Question 1, chap 16, sect 2.
part 1 of 2
10 points
A steel piano wire is 0
.
7 m long and has a
mass of 60 g. It is stretched with a tension of
600 N.
What is the speed of transverse waves on
the wire?
Correct answer: 83
.
666
m
/
s (tolerance
±
1
%).
Explanation:
Let :
F
= 600 N
,
L
= 0
.
7 m
,
and
m
= 60 g = 0
.
06 kg
.
The speed of transverse waves on the wire is
given by
v
=
radicalBigg
F
μ
=
radicaltp
radicalvertex
radicalvertex
radicalbt
F
m
L
=
radicalbigg
F L
m
=
radicalBigg
(600 N) (0
.
7 m)
0
.
06 kg
=
83
.
666 m
/
s
.
Question 2, chap 16, sect 2.
part 2 of 2
10 points
To reduce the wave speed by a factor of 2
without changing the tension, what mass of
copper wire would have to be wrapped around
the steel wire?
Correct answer: 180 g (tolerance
±
1 %).
Explanation:
Let :
v
v
′
= 2
,
and
m
= 60 g = 0
.
06 kg
.
The new wave speed will be
v
′
=
radicalbigg
F L
m
′
∝
radicalbigg
1
m
′
,
so
v
v
′
= 2 =
radicalbigg
m
′
m
m
′
= 4
m .
The amount of copper wire required is
Δ
m
=
m
′

m
= 3
m
= 3 (0
.
06 kg)
=
180 g
.
Question 3, chap 16, sect 2.
part 1 of 1
10 points
Tension is maintained in a string as in the
figure.
The observed wave speed is 25 m
/
s
when the suspended mass is 2
.
8 kg
.
The acceleration of gravity is 9
.
8 m
/
s
2
.
2
.
8 kg
What is the wave speed when the suspended
mass is 3 kg?
Correct answer: 25
.
8775 m
/
s (tolerance
±
1
%).
Explanation:
Let :
m
1
= 2
.
8 kg
,
m
2
= 3 kg
,
and
v
1
= 25 m
/
s
.
The linear density is
v
1
=
radicalBigg
F
μ
,
so
μ
=
F
v
2
1
(1)
=
m
1
g
v
2
1
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homework 33 – PAPAGEORGE, MATT – Due: Apr 19 2008, 4:00 am
2
=
(2
.
8 kg) (9
.
8 m
/
s
2
)
(25 m
/
s)
2
= 0
.
043904 kg
/
m
.
The velocity is
v
2
=
radicalBigg
F
μ
,
so
v
1
=
radicalbigg
m
2
g
μ
(2)
=
radicalBigg
(3 kg) (9
.
8 m
/
s
2
)
0
.
043904 kg
/
m
=
25
.
8775 m
/
s
.
AlternateSolution:
Plugging
μ
from Eq.
1 into Eq. 2, we have
v
1
=
radicalbigg
m
2
g
μ
(2)
=
radicalBigg
m
2
g v
2
1
m
1
g
=
v
1
radicalbigg
m
2
m
1
(3)
= (25 m
/
s)
radicalBigg
(3 kg)
(2
.
8 kg)
=
25
.
8775 m
/
s
.
Question 4, chap 16, sect 2.
part 1 of 3
10 points
A sonar signal of frequency 2
.
05
×
10
6
Hz
has a wavelength of 1
.
68 mm in water.
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 Spring '09
 KLEINMAN
 Physics, Mass, Work, Correct Answer, 1.1 rad, 1.68 mm, 1.8668 cm, 2.92503 cm

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