Consider a transverse wave travelling in four dimensions. This wave is propagating along the w axis, with amplitudes measured in the x,y, and z axes. This wave crosses our third dimension at a point (0, x1, y1, z1) perpendicularly. This wave would be manifested in our dimension as a pulsing sphere, with (x1,y1,z1) as the center of the sphere, and the amplitude of the wave as the radius of the sphere. For an analogy, consider a light wave propagating perpendiular to a sheet of paper, and the manifestation of the light wave on that sheet as line whose length varies as simple harmonic motion.

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