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When an earthquake occurs, it releases energy in the form of waves that travel through the Earth. These are known as seismic waves. Understanding these waves is crucial as they provide valuable information about the nature and location of earthquakes.
Earthquake waves are essentially divided into two main types: body waves and surface waves. Body waves travel through the Earth's interior and are further classified into Primary waves (P waves) and Secondary waves (S waves).
Earthquake waves help seismologists determine the epicenter of the earthquake. By analyzing the speed and path of these seismic waves, scientists can assess the potential impact area.

Primary waves, also known as P waves, are the fastest type of seismic waves generated by earthquakes. These waves move through the Earth at speeds of about 8 km/s.
P waves are compressional waves, meaning they push and pull particles in the direction the wave is moving. This is similar to the action of sound waves in air, which makes P waves able to travel through both solid rock and fluid mediums like water and air.
Due to their high speed, P waves are the first to be detected by seismographs. This characteristic helps seismologists quickly assess the occurrence of an earthquake and its intensity.

Secondary waves, or S waves, follow the primary waves during an earthquake and are slower, moving at approximately 4.5 km/s. Unlike P waves, S waves are transverse waves, which means they move the ground up and down or side to side, perpendicular to the direction of wave travel.
S waves can only move through solids, as liquids and gases do not support the shear stress that these waves create. This property gives important clues about the Earth's interior, such as the liquid nature of its outer core which refracts S waves.
S waves cause more damage than P waves due to their larger amplitude and slower speed, which means they shake the ground longer and more violently.

A seismograph is an instrument used to detect and record earthquake waves. It measures the motion of the ground caused by seismic waves as they travel through the Earth's surface.
Seismographs consist of a mass suspended on a spring, which remains stationary as the base of the instrument moves with the seismic waves. This relative motion is translated into a visual readout known as a seismogram.
When an earthquake occurs, a seismograph first records the faster P waves, followed by the slower S waves. This time difference is crucial as it helps calculate the distance from the seismograph to the earthquake's epicenter. The longer the time interval between the arrival of these waves, the further away the earthquake is located.

Understanding the relationship between speed, distance, and time is fundamental in seismology for locating earthquakes. The basic formula used is

• \[ d = v \times t \]

where \(d\) is distance, \(v\) is speed, and \(t\) is time.
In the case of earthquake waves, P and S wave speeds are known, and seismologists use the difference in arrival times at a seismograph to calculate the distance to the earthquake epicenter.
From the given exercise, the P wave arrives first, and 78 seconds later, the S wave follows. By using the speed of both waves and the time difference, the distance the waves traveled can be determined through solving the equations derived from their respective speeds, ultimately giving a measurement of 800 km to the earthquake's epicenter.