Morby, Grant – Homework 35 – Due: May 1 2006, noon – Inst: Drummond
1
This
printout
should
have
11
questions.
Multiplechoice questions may continue on
the next column or page – find all choices
before answering.
The due time is Central
time.
001
(part 1 of 1) 10 points
A standing wave is a superposition of two
harmonic waves described by
y
1
= 6 sin(
k x
+
ω t
)
,
and
y
2
= 6 sin(
k x

ω t
)
.
where
k
= 17
.
5929 m

1
and
ω
= 17
.
5929 s

1
.
Determine the smallest positive value of
x
corresponding to an antinode.
Correct answer: 8
.
92857 cm.
Explanation:
On a standing wave, the distance of the
nearest antinode and node is
d
=
λ
4
,
where
λ
is the wavelength.
In this problem,
x
= 0 is a node, which can be seen by adding
y
1
and
y
2
, and the wavelength is 2
π/k .
So the
smallest positive value of
x
corresponding to
an antinode is
x
=
π/
2
k .
002
(part 1 of 2) 10 points
A standing wave of frequency 5 hertz is set up
on a string 2 meters long with nodes at both
ends and in the center, as shown.
2 meters
Find the speed at which waves propagate
on the string.
1.
10 m
/
s
correct
2.
5 m
/
s
3.
2
.
5 m
/
s
4.
0
.
4 m
/
s
5.
20 m
/
s
Explanation:
Let :
f
= 5 Hz
and
λ
= 2 m
.
The wavelength is
λ
= 2 m, so the wave
speed is

~v

=
f λ
= (5 Hz)(2 m) =
10 m/s
.
003
(part 2 of 2) 10 points
Find the fundamental frequency of vibration
of the string.
1.
1 Hz
2.
7
.
5 Hz
3.
5 Hz
4.
10 Hz
5.
2
.
5 Hz
correct
Explanation:
2 meters
The fundamental wave has only two nodes
at the ends, so its wavelength is
λ
= 4 m and
the fundamental frequency is
f
=
v
λ
=
10 m
/
s
4 m
=
2.5 Hz
.
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 Spring '09
 KLEINMAN
 Physics, Work, Wavelength, Correct Answer, Standing wave, quarter wavelengths

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