Unsure if I should be using average velocity to solve this problem

[garcia1]

Homework Statement

The velocity of the transverse waves produced
by an earthquake is 6.96 km/s, while that of
the longitudinal waves is 12.0408 km/s. A
seismograph records the arrival of the trans-
verse waves 59.4 s after that of the longitudi-
nal waves.
How far away was the earthquake?
Answer in units of km.

Homework Equations

maybe v = x/t

The Attempt at a Solution

I'm honestly unsure of how to even go about this problem.

 

[gneill]

You have two things (signals) starting out at the same time and place and traveling at different velocities. What's the interval of time between their arrival at some destination a distance x away from where they began?

Concentrate on one signal at a time. Suppose that the distance happened to be x. How long would it take for the longitudinal wave to arrive?

 

[garcia1]

Their not looking for the time for longitudinal wave though, their looking for the distance from the start of the earthquake to the seismic pole. I'm still confused on how this can help.

 

[yster]

You need the time period to determine the distance. set up the equation that you gave for both waves and put the longitudinal waves times in terms of the transverse wave or vice versa. that reduces your number of unknowns to 2 then you have 2 equations with two unknowns. then it's just a matter of substituting.

 

[gneill]

Their not looking for the time for longitudinal wave though, their looking for the distance from the start of the earthquake to the seismic pole. I'm still confused on how this can help.

Perhaps it will become clear as we proceed. So, distance x; speed V_L = 12.0408 km/s, what's the time of travel t in terms of x and V_L?

 

[garcia1]

Is it t = x / 12.0408 km/s?

 

[gneill]

Is it t = x / 12.0408 km/s?

Yes it is. Let's call this t1.

Now do the same for the time it takes the transverse wave to arrive. Call that t2. What then, given these two expressions, is the difference in the arrival times?

 

[garcia1]

Is it T = t1- t2, or (x/12.0408 km/s) - (x/6.96 km/s)?

 

[gneill]

Is it T = t1- t2, or (x/12.0408 km/s) - (x/6.96 km/s)?

Sure. I might write it as T = t2 - t1 so that the resulting ΔT will be positive; the faster signal will arrive first. Match up the variables in the equation with the values you are given in the problem statement. Can you rearrange the equation to solve for what you want?