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

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

Answers ( )

    0
    2021-09-01T16:19:12+00:00

    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.

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