# Q.15.26 Earthquakes generate sound waves inside the earth. Unlike a gas, the earth can experience both transverse (S) and longitudinal (P) sound waves. Typically the speed of S wave is about $4.0\: km\: s^{-1}$, and that of P wave is $8.0\: km\: s^{-1}$. A seismograph records P and S waves from an earthquake. The first P wave arrives 4 min before the first S wave. Assuming the waves travel in straight line, at what distance does the earthquake occur?

Let us assume the earthquake occurs at a distance s.

$\\\Delta t=4\times 60=240s\\ \Delta t=\frac{s}{v_{s}}-\frac{s}{v_{p}} \\\Delta t=\frac{s}{4}-\frac{s}{8}\\ 240=\frac{s}{8}\\ s=1960km$

The origin of the earthquake is at a distance of 1960 km.

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