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Let's say you create a pulse on a string. The wave moves in 1d(in a straight line) but the particles of the string itself extend into 2 dimensions. The same goes for ripples in water. The wave traverses in the plane but the ripples come out of the plane. Now what if there is a 3d wavefront ( Any point source of light would serve as an example. ) so extending the analogy.. Are the particles going into 4th dimension? I know that they aren't. But why?

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I think there are a couple of points of confusion here. Firstly, the particles in a wave on a string or in water oscillate perpendicularly to the wave's direction of travel, but this is not a requirement for wave motion. Consider for example a sound wave travelling through air - air molecules oscillate in the same direction as the wave moves. Waves where the oscillations are perpendicular to the direction of travel are transverse waves; those with oscillations parallel to the direction of travel are longitudinal.

To answer your direct question, a transverse wave is possible in three dimensions without requiring a fourth. For example, the polarisation vector of an electromagnetic wave travelling in, say, the $z$ direction, oscillates in the $x$ and $y$ direction.

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  • $\begingroup$ Ah but what if there is a way to create a transverse wave in 3d? Would the particles then oscillate perpendicular to all three axis? Is that even possible? $\endgroup$ Commented Jun 9, 2019 at 14:33
  • $\begingroup$ As far as we can observe there are only three spatial dimensions, so there is no fourth dimension for particles to oscillate in. It has been proposed that gravitational waves oscillate in more than three dimensions, but data from the LIGO experiment pretty much rules this out. $\endgroup$
    – DavidH
    Commented Jun 9, 2019 at 14:48
  • $\begingroup$ In other words, while there's nothing wrong with the idea of particles oscillating in 4 spatial dimensions, we don't see any experimental evidence that that is the case. Of course, many string theories call for 10 or more spatial dimensions, so who knows what we'll see as we keep peering deeper into the universe. Maybe we will find the whispers of those dimensions, maybe we wont! $\endgroup$
    – Cort Ammon
    Commented Jun 9, 2019 at 15:45
  • $\begingroup$ Your answer is not supported by your example. Nothing actually moves perpendicular to the direction of the electromagnetic wave. Sure the intensity of the field is perpendicular, but it does not represent movement of any particles or anything at all in this direction. A true example of a transverse wave with particles actually moving perpendicularly is a transverse sound wave in solid materials. $\endgroup$
    – safesphere
    Commented Jun 9, 2019 at 15:57
  • $\begingroup$ While there is no movement of matter perpendicular to the wave, there is still oscillation in this direction - just of the polarisation vector of the EM field. Electromagnetic waves are certainly transverse. $\endgroup$
    – DavidH
    Commented Jun 9, 2019 at 15:59

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