Final answer:
Seismologists use the arrival times of P-waves and S-waves, which travel at different speeds, to locate earthquake epicenters. By measuring the time difference between these waves and knowing their speeds, the distance to the earthquake's source can be calculated with a certain precision.
Step-by-step explanation:
Seismographs measure the time difference between the arrival of P-waves, which are the fastest and first to arrive, and S-waves, which are slower and arrive afterward. Knowing the speeds at which these waves travel through the Earth's crust (P-waves at 4.00 to 7.20 km/s and S-waves at 2.00 to 5.00 km/s), seismologists can calculate the distance to the earthquake's epicenter. The precision of this measurement is tied to the accuracy of the arrival time recordings.
If the seismographs can measure time with a precision of 0.100 s, and knowing the differential speeds of P-waves and S-waves, one can calculate how precisely seismologists can determine the distance to an earthquake's source. In the given example, if P-wave speed is 7.20 km/s and S-wave speed is 4.00 km/s, the time difference between their arrival will directly relate to the distance to the earthquake's epicenter. This is also crucial in detecting underground nuclear test explosions, as similar principles apply. However, any uncertainty in wave propagation speeds increases the uncertainty in the determination of the epicenter.