Question

Earthquakes are essentially sound waves—called seismic waves—traveling through the earth. Because the earth is solid, it can support both longitudinal and transverse seismic waves. The speed of longitudinal waves, called P waves, is 8000 m/s. Transverse waves, called S waves, travel at a slower 4500 m/s. A seismograph records the two waves from a distant earthquake. The S wave arrives 2.0 min after the P wave. Assume that the waves travel in straight lines, although actual seismic waves follow more complex routes. If the S wave arrives 2.3 min after the P wave, how far away was the earthquake?

Answer 1

Answer:

1230 km  

Explanation:

From the time delay, we can write:

$t_{s} -t_{p} =$Δt

Knowing that t =$\frac{d}{v}$  we rewrite the formula as  

$\frac{d}{vs} -\frac{d}{vp} =d(\frac{1}{vp}-\frac{1}{vs} )$=Δt

From this we can find the distance to be  

$d=\frac{v_{s} v_{p} }{v_{p}-v_{s} }$*Δt

   = 1230 km