Final Answer:
The distance to the epicenter of an earthquake is determined by the time interval between P-waves and S-waves.Thus the option c) By the time interval between P-waves and S-waves is correct.
Step-by-step explanation:
The time interval between the arrival of P-waves (primary or compressional waves) and S-waves (secondary or shear waves) at a seismograph station is crucial for determining the distance to the earthquake epicenter.
P-waves travel faster than S-waves, and the time gap between their arrivals increases with distance from the epicenter. This relationship is described by the formula Distance=Velocity×Time, where the velocity is the speed of the seismic waves and the time is the interval between the arrivals of P and S-waves.
Seismic waves travel through the Earth at known velocities, and by measuring the time difference between the arrivals of P and S-waves on a seismogram, seismologists can calculate the distance from the earthquake epicenter to the seismograph station. The greater the time difference, the farther the station is from the epicenter.
Multiple seismograph stations are often used to triangulate the exact location of the epicenter. This method is based on the fact that seismic waves travel through the Earth at different speeds depending on the type of material they pass through, providing valuable information about the Earth's interior structure.
In summary, option (c) correctly identifies the method for determining the distance to the epicenter of an earthquake, involving the measurement of the time interval between the arrivals of P-waves and S-waves, which is fundamental to seismology and earthquake monitoring.
Thus the option c) By the time interval between P-waves and S-waves is correct.