What is the average speed of the S wave in an earthquake?

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SUMMARY

The average speed of the S wave in an earthquake can be calculated using the time difference between the arrival of P waves and S waves. In this case, the P wave travels at an average speed of 8.0 km/s and arrives 42 seconds before the S wave at a distance of 1000 km from the epicenter. The average speed of the S wave is determined to be 5.0 km/s, calculated by using the formula for speed, distance, and time. This conclusion is reached by recognizing that the S wave takes longer to travel the same distance due to its slower speed compared to the P wave.

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  • Understanding of seismic wave types: Primary (P) and Secondary (S) waves
  • Basic knowledge of speed, distance, and time relationships
  • Familiarity with wave properties, including frequency and wavelength
  • Ability to apply algebraic equations to solve for unknowns
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Students studying geology, seismology, or physics, as well as professionals involved in earthquake research and engineering, will benefit from this discussion.

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Homework Statement



Assume that P and S (Primary and Secondary) waves from an earthquake with a focus near the Earth's surface travel through the Earth at nearly constant but different average speeds. A monitoring station that is 1000 km from the epicenter detected the S wave to arrive at 42 seconds after the arrival of the P wave. If the P wave has an average speed of 8.0 km/s, what is the average speed of the S wave?


Homework Equations


v = Lambda/T
or
v= Lambda * f


The Attempt at a Solution



The period of the wave should be 42 seconds which would make the frequency : 1/42 or .0238

If the velocity is 8.0 km/s then to find Lambda you would have to:
8 = lambda * .0238 which makes Lambda 336.13

Where I get confused is when I multiply, 336.13 * .023, I get an answer of 8 again which would be the velocity of the primary wave. I assume that there is a new frequency that needs to be used in the equation, but I can't seem to figure it out. Any help would be great. Thanks.
 
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This has nothing to do with frequencies and wavelengths and everything to do with speeds and distances. Replace the waves with cars and see what you get.
 

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