Earthquakes generate sound waves inside Earth. Unlike a gas, Earth can experience both transverse (S) and longitudinal (P) sound waves. Typically, the speed of S waves is about 4.5 km/s, and that of P waves 80 km/s. A seismograph records P and S waves from an earthquake.The first P waves arrive 3.0 min before the first S waves.If the waves travel in a straight line, how far away did the earthquake occur?

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Cavalascamq · Accepted Answer

Given:  △  t = 3min.      v          s        =  4.5  k  m      /    s         v          p        =  8  k  m      /    sSince both the transverse and the longitudinal waves travel in a straight line the same exact distance, therefore we have the ratio  D  =      v          s            t          s        =      v          p            t          p      By substitution we have            v              s                    v              p              =            t              p                    t              s              =      4.5    8    =  0.5625Therefore we have       t          p        =  0.5625      t          p      Since  △  t  =      t          s        −      t          p        =  3  ×  60  =  180  sBy solving the 2 equations for       t          s       we have      t          s        −  0.5625      t          s        =  0.4375      t          s        =  180      t          s        =  411.4  sBy substitution to find the distance covered by both waves  d  =      v          s        ×      t          s        =  4.5  ×  411.42  =  1851.42  k  mResult:d= 1851.42km

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