Return to 4D Transverse Wave (idea)

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].