Final answer:
The fastest wave that moves in a push-pull fashion is the P-wave, which travels at speeds between 4 to 7 km/s in granite and is faster than S-waves. These waves, also known as pressure or compressional waves, are the first detected after earthquakes.
Step-by-step explanation:
The wave that travels fastest and moves in a push-pull fashion of alternating pulses of compression (push) and extension (pull) is the P-wave. These waves, also known as compressional or pressure waves, can propagate through various types of mediums, including solids, liquids, and gases. P-waves are the first waves to be detected by seismographs after an earthquake occurs due to their high speed, which ranges from 4 to 7 km/s in granite. They have the characteristic of getting progressively farther ahead of S-waves, or shear waves, which move at a slower speed ranging from 2 to 5 km/s. The ability to differentiate between P-waves and S-waves is crucial when analyzing seismic events, as it allows geologists to determine the distance to the epicenter of an earthquake.