Wavelength - how far away did earthquake occur

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Homework Help Overview

The discussion revolves around calculating the distance to an earthquake based on the arrival times of P and S waves detected by a seismic station. The problem involves understanding wave speeds and the time difference between the two types of seismic waves.

Discussion Character

  • Mathematical reasoning, Problem interpretation, Assumption checking

Approaches and Questions Raised

  • Participants explore equations relating wave speed, distance, and time, attempting to derive expressions for distance based on the time difference of 1 minute between wave arrivals. Some participants question the algebraic steps taken to manipulate the equations.

Discussion Status

The discussion is active, with participants providing various algebraic manipulations and checking each other's reasoning. Some guidance has been offered regarding the relationships between the variables involved, but no consensus has been reached on the final solution.

Contextual Notes

Participants are working under the assumption that the speeds of P and S waves are constant and are questioning how to correctly relate the time difference to the distance traveled by the waves.

mathcrzy
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Homework Statement



Assuming typical speeds of 8.9 km/s and 5.8 km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 1.0 min apart?
_____km


Homework Equations



v=(lamba)(f)
1/T=frequncy
lamba=one wave length
T=period

X=same

Vpwave=deltaX/T

Vswave=dletaX/T+60

The Attempt at a Solution



8.9=

5.8=
 
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mathcrzy said:
Vpwave=deltaX/T = 8.9 km/sec

Vswave=dletaX/T+60 = 5.8 km/sec

This is basically what you need. Solve the first equation for an expression for T and substitute it into the second equation, so you can eliminate the unknown T. You now have an equation you can solve for deltaX.

[As a check, consider this. Both types of waves started from the same "source". About how much do the P-waves gain on the S-waves each second? How much longer do the S-waves need to make up the difference? How long will it take for the S-waves to be a full minute behind? How far will the P-waves have traveled in that time? The algebraic solution described above is equivalent to answering these questions.]
 
Last edited:
Vp=deltaX/T
VpT=deltaX
T=deltaX/Vp

Vs=deltaX/T+60
Vs(T+60)=deltaX
VsT+Vs60=deltaX
T=deltaX-Vs60/Vp

deltaX-Vs60/Vp=deltaX/Vp
deltaX-Vs60=deltaX
deltaX=Vs60

Is this how you solve for deltaX
 
mathcrzy said:
Vp=deltaX/T
VpT=deltaX
T=deltaX/Vp

Vs=deltaX/T+60
Vs(T+60)=deltaX
VsT+Vs60=deltaX

You were OK to here. The next line would then be

T = (deltaX - Vs·60)/Vs ,

so from there,

(deltaX - Vs·60)/Vs=deltaX/Vp

(deltaX/Vs) - (deltaX/Vp) = 60

(deltaX) · [ (1/Vs) - (1/Vp) ] = 60

delta X = [ (Vs·Vp) / (Vp - Vs) ] · 60
 
i got the answer but just wondering how you got from:

(deltaX - Vs·60)/Vs=deltaX/Vp

to

(deltaX/Vs) - (deltaX/Vp) = 60
 
(deltaX - Vs·60)/Vs = deltaX/Vp

(deltaX)/Vs - (Vs·60)/Vs = deltaX/Vp

(deltaX)/Vs - (60) = deltaX/Vp

(deltaX/Vs) - (deltaX/Vp) = 60

In fact, you could really start right from here because this just says that the difference between the time it takes the S-waves to reach the station and the time it takes for the P-waves to do so is 60 seconds.
 

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