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Earth quake waves are also called as seismic waves.
they are of three types:
1)primary or P waves or longitudinal waves  [to and fro motion]  (fastest of all) {pass through solids,liquids and gases}
2)secondary or S waves or shear or transverse waves  [vibrate at right angles to direction of propagation] {pass only through solids}
3)L or surface waves--->Rayleigh waves[in elliptical orbits] and love waves[horizontal and 90 deg to their direction of movement]  (lower velocity of all)
u could observe the different types of waves in the given figure:
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Earthquake waves are also called seismic waves. These waves are of three types. These are:
1. Primary or P waves are push and pull waves.
2. Secondary, S or Shear Waves are also called transverse wave.
3. L or Surface Waves reach the earth's surface after P and S waves .There are two types of L waves: (i) Raileigh Waves (ii) Love Waves. 
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