salazar (ggs332) – HW12 – TSOI – (58160)
1
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printout
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have
22
questions.
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before answering.
001
10.0 points
Radio waves travel at the speed of light:
3
×
10
5
km
/
s.
What is the wavelength of radio waves re
ceived at 98
.
3 MHz on your FM radio dial?
Correct answer: 3
.
05188 m.
Explanation:
Let :
v
= 3
×
10
5
km
/
s
= 300 million m
/
s
and
f
= 98
.
3 MHz
= 98
.
3 million Hz
.
λ
=
v
f
=
300 million m
/
s
98
.
3 million Hz
=
3
.
05188 m
.
002
10.0 points
Earthquakes produce two kinds of seismic
waves: he longitudinal
primary
waves (called
P
waves) and the transverse
secondary
waves
(called
S
waves). Both S waves and P waves
travel through Earth’s crust and mantle, but
at different speeds; the P waves are always
faster than the S waves, but their exact speeds
depend on depth and location. For the pur
pose of this exercise, we assume the P wave’s
speed to be 8410 m
/
s while the S waves travel
at a slower speed of 4640 m
/
s.
If a seismic station detects a P wave and
then 94
.
8 s later detects an S wave, how far
away is the earthquake center?
Correct answer: 981
.
253 km.
Explanation:
Let :
v
P
= 8410 m
/
s
,
v
S
= 4640 m
/
s
,
and
Δ
t
= 94
.
8 s
.
Suppose the earthquake happens at time
t
= 0
at some distance
d
.
The P wave and the
S wave are both emitted at the same time
t
= 0, but they arrive at different times, re
spectively
t
P
=
d
v
P
and
t
S
=
d
v
S
. The S wave
is slower, so it arrives later than the P wave,
the time difference being
Δ
t
=
d
v
S

d
v
P
=
d
(
v
P

v
S
)
v
P
v
S
.
Consequently, given this time difference and
the two waves’ speeds
v
P
and
v
S
, the earth
quake center is
d
=
v
P
v
S
Δ
t
v
P

v
S
=
(8410 m
/
s) (4640 m
/
s) (94
.
8 s)
8410 m
/
s

4640 m
/
s
·
1 km
1000 m
=
981
.
253 km
away from the seismic station.
003
(part 1 of 2) 10.0 points
A wave moving along the
x
axis is described
by
y
(
x, t
) =
A e
−
(
x
+
vt
)
2
/b
where
x
is in meters,
t
is in seconds,
A
= 3 m,
v
= 5 m
/
s, and
b
= 4 m
2
.
Determine the speed of the wave.
Correct answer: 5 m
/
s.
Explanation:
y
(
x, t
) =
A e
−
(
x
+
vt
)
2
/b
is of the form
y
(
x, t
) =
f
(
x
+
v t
)
so it describes a wave at
v
=
5 m
/
s
.
004
(part 2 of 2) 10.0 points
Determine the direction of the wave.
1.
+
x
direction
2.

x
direction
correct
3.
+
y
direction
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salazar (ggs332) – HW12 – TSOI – (58160)
2
4.

y
direction
Explanation:
f
(
x
+
v t
) =
f
(
x

(

v
)
t
)
so the wave is moving at

5 m
/
s (in the
negative direction).
005
(part 1 of 2) 10.0 points
The time interval indicated on this diagram is
G
.
+
S
0

S
0
S
t
(seconds)
→
G
Which formula corresponds best to the di
agram?
1.
S
(
t
) =
S
0
sin
parenleftbigg
2
π t
G
parenrightbigg
2.
S
(
t
) =
S
0
sin
parenleftbigg
t
2
π G
parenrightbigg
3.
S
(
t
) =
S
0
sin
parenleftbigg
t
3
π G
parenrightbigg
4.
S
(
t
) =
S
0
sin
parenleftbigg
2
t
3
π G
parenrightbigg
5.
S
(
t
) =
S
0
sin
parenleftbigg
2
π t
3
G
parenrightbigg
6.
S
(
t
) =
S
0
sin
parenleftbigg
3
π t
2
G
parenrightbigg
7.
S
(
t
) =
S
0
sin
parenleftbigg
2
t
3
G
parenrightbigg
8.
S
(
t
) =
S
0
sin
parenleftbigg
3
t
2
π G
parenrightbigg
9.
S
(
t
) =
S
0
sin
parenleftbigg
3
t
2
G
parenrightbigg
10.
S
(
t
) =
S
0
sin
parenleftbigg
3
π t
G
parenrightbigg
correct
Explanation:
The equation of a wave with zero displace
ment at the origin is given by
S
(
t
) =
S
0
sin(
ω t
) =
S
0
sin
parenleftbigg
2
π
T
t
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 Spring '10
 TSOI
 Physics, Light, Sin, Correct Answer, Salazar

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