You will need to know about body waves, as they tell us so much about what we cannot see inside the planet.
Primary waves are longitudinal waves that push and pull the earth. They are the fastest body wave, averaging speeds of about 6 km/s, so arrive first.
S-wavesSecondary waves are transverse waves, which make the earth shake from side to side. Slower than P waves, they average about 4 km/s so arrive second.