Chapter 16, Problem 56PE

(a) Seismographs measure the arrival times of earthquakes with a precision of 0.100 s. To get the distance to the epicenter of the quake, they compare the arrival times of S− and P−waves, which travel at different speeds. Figure 16.48) If S− and P−waves travel at 4.00 and $\text{7}.\text{2}0\text{ km}/\text{s}$, respectively, in the region considered, how precisely can the distance to the source of the earthquake be determined? (b) Seismic waves from underground detonations of nuclear bombs can be used to locate the test site and detect violations of test bans. Discuss whether your answer to (a) implies a serious limit to such detection. (Note also that the uncertainty is greater if there is an uncertainty in the propagation speeds of the S− and P—waves.)

Figure 16.48 A seismograph as described in above problem. (credit: Oleg Alexandrov)