practice 13 – ALIBHAI, ZAHID
1
Latest unpenalized work: Apr 22 2007 Sunday
04:00 (after this date you can not make a
perfect score).
Work cutoff:
Apr 22 2007,
4:00 am.
Question 1
part 1 of 3
10 points
Two waves in one string are described by
the relationships
y
1
=
A
1
cos(
k
1
x

ω
1
t
)
y
2
=
A
2
sin(
k
2
x

ω
2
t
)
where
A
1
= 2
.
2 cm,
A
2
= 2
.
7 cm,
k
1
=
6
cm
−
1
,
k
2
=
4
cm
−
1
,
ω
1
=
3
rad
/
s,
ω
2
= 4 rad
/
s,
y
and
x
are in centimeters,
and
t
is in seconds.
Find the superposition of the waves
y
1
+
y
2
at the position
x
1
= 0
.
5 cm and time
t
1
= 2 s.
Answer in units of cm.
Question 2
part 2 of 3
10 points
Find the superposition of the waves
y
1
+
y
2
at the position
x
2
= 1 cm and time
t
2
= 0
.
7 s.
Answer in units of cm.
Question 3
part 3 of 3
10 points
Find the superposition of the waves
y
1
+
y
2
at the position
x
3
= 0
.
5 cm and time
t
3
=

0
.
38 s.
Answer in units of cm.
Question 4
part 1 of 2
10 points
Two sound sources radiating in phase at a
frequency of 540 Hz interfere such that max
ima are heard at angles of 0
◦
and 24
◦
from
a line perpendicular to that joining the two
sources.
The velocity of sound is 340 m/s.
y
L
d
S
1
S
2
θ
listening
direction
θ
δ
Find
the
separation
between
the
two
sources.
Answer in units of m.
Question 5
part 2 of 2
10 points
Find the next larger angle at which a max
imum intensity will be heard.
Answer in units of
◦
.
Question 6
part 1 of 1
10 points
A light string of mass
per unit
length
8
.
62 g
/
m has its ends tied to two walls sepa
rated by a distance equal to three fourths the
length
L
of the string as shown in the figure.
A mass
m
is suspended from the center of the
string, applying a tension in the string.
The acceleration of gravity is 9
.
8 m
/
s
2
.
3
L
4
m g
L
2
L
2
θ
θ
What size mass should be suspended from
the
string
to
produce
a
wave
speed
of
88
.
9 m
/
s?
Answer in units of kg.
Question 7
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practice 13 – ALIBHAI, ZAHID
2
part 1 of 1
10 points
An incident sine wave
y
i
(
x, t
) =
A
sin(
k x

ω t
)
(1)
travels to the right and is reflected off a fixed
end of the string at
x
=
L
.
Which of the following expression gives the
correct formula for the reflected wave
y
r
(
x, t
)?
1.
y
r
(
x, t
) =
A
sin(
k x
+
ω t
+ 2
k L
)
2.
y
r
(
x, t
) =
A
sin(
k x
+
ω t
)
3.
y
r
(
x, t
) =
A
sin(
k x
+
ω t

k L
)
4.
y
r
(
x, t
) =
A
sin(
k x

ω t
+ 2
k L
)
5.
y
r
(
x, t
) =
A
sin(
k x

ω t
)
6.
y
r
(
x, t
) =
A
sin(
k x
+
ω t

2
k L
)
7.
y
r
(
x, t
) =
A
sin(
k x

ω t

2
k L
)
8.
y
r
(
x, t
) =
A
sin(
k x
+
ω t
+
k L
)
9.
y
r
(
x, t
) =
A
sin(
k x

ω t
+
k L
)
10.
y
r
(
x, t
) =
A
sin(
k x

ω t

k L
)
Question 8
part 1 of 1
10 points
You are given
f
1
(
x
), a transverse wave that
moves on a string that ends and is FIXED in
place at
x
= 5 m. As the problem begins, the
wave is moving to the right at
v
= 1 m/s.
v
0
1
2
3
4
5
3
2
1
0
1
2
3
Amplitude (centimeter)
Distance (meter)
What is the shape of the wave on the string
after 5 s?
1.
0
1
2
3
4
5
3
2
1
0
1
2
3
Distance (meter)
2.
0
1
2
3
4
5
3
2
1
0
1
2
3
Distance (meter)
3.
0
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 Spring '08
 Turner
 Work, ZAHID Latest

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