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

In summary: Yes, you can rearrange the equation to solve for what you want. Let's call the result T. T = 6.96 - 12.0408 = 4.1208 km/s.
  • #1
garcia1
27
0

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.
 
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  • #2
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?
 
  • #3
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.
 
  • #4
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.
 
  • #5
garcia1 said:
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 VL = 12.0408 km/s, what's the time of travel t in terms of x and VL?
 
  • #6
Is it t = x / 12.0408 km/s?
 
  • #7
garcia1 said:
Is it t = x / 12.0408 km/s?

Yes it is. :smile: 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?
 
  • #8
Is it T = t1- t2, or (x/12.0408 km/s) - (x/6.96 km/s)?
 
  • #9
garcia1 said:
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?
 

1. What is average velocity and how is it different from other types of velocity?

Average velocity is a measurement of an object's overall displacement over a period of time. It takes into account both the distance traveled and the time taken to travel that distance. Other types of velocity, such as instantaneous velocity, only measure an object's velocity at a specific moment in time.

2. When should I use average velocity to solve a problem?

Average velocity is best used when you want to determine an object's overall velocity over a period of time. For example, if you want to know how fast a car traveled during a road trip, you would use average velocity. However, if you want to know the car's velocity at a specific moment, you would use instantaneous velocity.

3. How do I calculate average velocity?

Average velocity is calculated by dividing the total displacement by the total time taken. The formula is: average velocity = total displacement / total time. Make sure to use the same units for both distance and time in your calculation.

4. Can I use average velocity for objects with changing velocities?

Yes, you can still use average velocity for objects with changing velocities. However, the average velocity will only give you an overall measurement and may not accurately represent the object's motion at a specific moment. For objects with changing velocities, it is best to use other types of velocity, such as instantaneous velocity, to get a more accurate picture of its motion.

5. Are there any limitations to using average velocity?

One limitation of average velocity is that it does not take into account the direction of motion. It only measures the overall distance and time, not the actual path an object takes. Additionally, average velocity may not accurately represent an object's motion if it has changing velocities or accelerations. In these cases, other types of velocity may be more appropriate to use.

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