## 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?
Mi

in progress 0
6 months 2021-09-01T16:18:04+00:00 1 Answers 2 views 0

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.