Wave race: Help me start off the earthquakes

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Homework Help Overview

The problem involves calculating the distance to an earthquake based on the arrival times of transverse and longitudinal waves, with given velocities for each type of wave. The original poster attempts to understand the relationship between the wave speeds and the time difference in their arrivals.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss using the relationship between distance, speed, and time to set up equations for both wave types. There are attempts to express the time for the transverse wave and how it relates to the longitudinal wave's arrival time.

Discussion Status

Some participants have offered hints and guidance on how to set up the equations without needing to know the exact time for the transverse wave. The discussion has evolved with various interpretations and attempts to clarify the setup of the problem.

Contextual Notes

There is mention of confusion regarding the time values and how they relate to the velocities of the waves. The original poster expresses uncertainty about the calculations and the overall approach to the problem.

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Homework Statement


The velocity of the transverse waves produced by an earthquake is 8.9km/s while that of the longitudinal waves is 5.1km/s. A seismograph records the arrival of the transverse waves 73s before that of the longitudinal waves. How far away was the earthquakes?

Homework Equations


http://tpub.com/content/neets/14191/img/14191_46_1.jpg
displacement= (Initial Velocity)(Time) + (0.5)(a)(time squared)?

The Attempt at a Solution


Given Answer: 8.7x10^2 km=870km=870,000m
I wish I showed you guys the 12/13 problems out of this worksheet that I did to show that I did try and am not trying to mooch..

I scoured the internet and found some similar links..
http://www.glenbrook.k12.il.us/gbssci/phys/p163/ec/u10ec.html
https://www.physicsforums.com/showthread.php?t=88686
http://www.hopperinstitute.com/phys_waves.html

My last link basically showed.. they multiplied the fastest velocity by 98s.. How did they get 98s..I don't know..

Can anyone get me started on this?
==
I've tried..
3.8km (difference in velocity displacement)=73s*x
x=52m/2 .. Then try and use displacement formula.. But I have no acceleration value, so meh..
 
Last edited by a moderator:
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The waves move at constant speed--no need for accelerated motion, just distance = speed*time.

Try this: Call the distance D; call the time for the transverse wave to arrive T. Now apply the above speed equation for each wave and solve for D.
 
Sorry.. it's not clicking.. How do I find the time for the transverse wave to arrive?
 
You don't need the time, just call it T. Write two equations: one for the transverse wave; one for the longitudinal. You'll be able to eliminate T and solve for D.

Hint: If the time for the transverse wave is T, what's the time for the longitudinal wave?
 
T + 72s? :-)
===
PS, distance = speed*time is (at least in this case) the same as displacement=velocity*time ?
We haven't done much of speed at all.. So I'm more comfortable with delta d:D
===
I've done 5.1 (km/s) + T=delta d=8.9 (km/s) + T + 72s
=5.1 (km/s)=delta d=8.9 (km/s) + 72s..

That can give me 3.8 km/s=72s..
 
Last edited:
pugfug90 said:
T + 72s?
Of course. :smile:
PS, distance = speed*time is (at least in this case) the same as displacement=velocity*time ?
Same thing.
 
kk
So how do I resolve 3.8 km/s = 72s = delta d?
 
Last edited:
I think I did my math wrong.. Ignore post#5..
Hey I think I got it! But this problem is so convoluted I'm going to forget it all meh rawr. PS, want to check my method? (I know the answer)
==
D=(8.9km*T)/s = [(5.1km)(T+72s)]/s
They both have same denominator so that cancels..
8.9km*T=5.1km*T + 367.2km*s
3.8km*T=367.2km*s
Isolate T..
T=(367.2km*s)/(3.8km)=~96.6s
That means it takes the transverse (faster), 96.6s to get there, and ~170s for the other..
I can use each's respective time and velocity to find distance.. Thanks Doc Al! I think I got it.
 

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