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Two important types of waves include longitudinal waves and what other kind?

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transverse

Like transverse waves, longitudinal waves are mechanical waves, which means they transfer energy through a medium. Unlike transverse waves, longitudinal waves cause the particles of medium to move parallel to the direction of the wave. They are most common in springs, where they are caused by the pushing an pulling of the spring. Although the surface waves on water are transverse waves, fluids  liquids, gases, and plasmas  usually transmit longitudinal waves.

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