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Algebra/transverse waves

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Question
why can transverse waves be thought of as two waves a wave in time and a wave in space?  

Answer
It's really just one wave but you can consider it mathematically two ways.  Have you been to a beach and seen waves come in?   Those are transverse waves.  The waves appear to move in toward the beach.  But if you're standing out in the water at a certain spot, you know that the water simply moves up and down where you are.  In other words, the amplitude of the wave increases and decreases as a function of time at a point in space.  

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