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 PP waves, is 8000 m/sm/s. Transverse waves, called SS waves, travel at a slower 4500 m/sm/s. A seismograph records the two waves from a distant earthquake. The SS wave arrives 2.0 minmin after the PP wave. Assume that the waves travel in straight lines, although actual seismic waves follow more complex routes.

Answer 1

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 PP wave.How far away is the Earthquake.  Assume that the waves travel in straight lines, although actual seismic waves follow more complex routes.

Answer:

The distance is  $d = 1.23 *10^{6} \ m$

Explanation:

From the question we are told that

   The speed of longitudinal seismic  wave is  $v_p = 8000 \ m/s$

    The speed of Transverse seismic  wave is  $v_s = 4500 \ m/s$

     The time difference between the arrival of longitudinal seismic with respect to Transverse waves is  $\Delta t = 2.0\ min = 120\ seconds$

Generally the  time difference between the arrival of longitudinal seismic with respect to Transverse waves is mathematically represented as

     $\Delta t = t_p - t_s$

=>  $\Delta t =\frac{d}{v_p} -\frac{d}{v_s}$

=>   $d = \frac{\Delta t}{ \frac{1}{v_p} - \frac{1}{v_s} }$

=>   $d = \frac{120 }{ \frac{1}{8000} - \frac{1}{4500} }$

=>   $d = 1.23 *10^{6} \ m$