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

[laxboi33]

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.

 

[ideasrule]

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.