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Earthquakes produce two kinds of seismic waves: he longitudinal primary waves (called P waves) and the transverse secondary wave
Question
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 8560 m/s while the S waves travel
at a slower speed of 5760 m/s.
If a seismic station detects a Pwave and
then 30.5 s later detects an S wave, how far
away is the earthquake center?
Answer in units of km.
Mi
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Physics
4 years
2021-09-01T16:18:04+00:00
2021-09-01T16:18:04+00:00 1 Answers
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Answers ( )
Answer:
d
=
s
t
Explanation:
distance = speed * time
here, the distance is from the earthquake centre to the seismic station.
both the P and S waves travel from the earthquake centre before being detected by the seismic station, so the distance is the same for both.
the speeds are given as
8740
m
/
s
for the P wave and
4100
m
/
s
for the S wave.
we also know that the P wave arrives
47.4
seconds before the S wave.
we do not know the time that the P wave takes to travel, but we can denote it as
t
P
.
the time that the S wave takes to travel can be denoted as
t
P
+
47.4
, where time is in seconds.
for the S wave, speed * time is
4100
⋅
(
t
P
+
47.4
)
for the P wave, speed * time is
8740
⋅
t
P
.
since the distances that they travel are the same, the two expressions for speed * time are equal.
4100
⋅
(
t
P
+
47.4
)
=
8740
⋅
t
P
if you expand the brackets, you can find that
4100
t
P
+
194340
=
8740
t
P
then you can subtract
4100
t
P
:
4640
t
P
=
194340
and divide by
4640
to find
t
P
, which is the time that P takes to travel:
t
P
=
41.883
…
seconds
since distance = speed * time, the distance that the P wave travels is
t
P
⋅
the speed of P.
this is
41.883
s
⋅
8740
m
/
s
, which gives
366057.42
m
.
in kilometres, this is
366
k
m
to
3
significant figures.