Final answer:
During an earthquake, P-waves (longitudinal waves) travel faster than S-waves (transverse waves), allowing them to arrive first at seismograph stations. The known speeds of P and S waves enable the estimation of the epicenter's distance by calculating their arrival time difference. This is crucial for early warning systems and gauging the earthquake's impact.
Step-by-step explanation:
When a P-wave passes through Earth during an earthquake, it moves in a longitudinal fashion (compressing and expanding the material it travels through) at speeds between 4 to 7 km/s depending on the rigidity of the material. In contrast, S-waves which are transverse, travel at slower speeds of 2 to 5 km/s. P-waves are known to arrive first at seismograph stations because they are faster. Knowledge of the speed differential between P-waves and S-waves allows geologists and seismologists to calculate the time difference in their arrival at a seismograph station and thereby estimate the distance to the earthquake's epicenter.
For instance, if P-waves outrun S-waves by a speed of v = 3.20 km/s; and the uncertainty in the distance (Ad) is found to be 0.320 km, this value is pondered along with uncertainties in the velocities to estimate the distance to the source of the seismic activities, such as an earthquake or a nuclear detonation. Notably, the fact that S-waves are more damaging than P-waves and that surface waves are the most damaging of all seismic waves is critical for emergency preparedness and public safety. By calculating the arrival time difference between P- and S-waves, residents can be given a warning about the impending stronger shaking caused by the S-waves.