Question about waves;

	A friend of mine is a physics concentrator and we discussed some of the principals of waves in relation to dimensions.  What we discovered is an extract from Walter Strauss's book "Partial Differential Equations" which addresses how waves behave in different dimensions;

			Huygens's principle [a principle that allows us to see sharp images or hear any sound that is carried through the air without echoes] is false in two dimensions.  For instance, when you drop a pebble onto a calm pond, surface waves are created which (approximately) satisfy the two dimentional wave equation with a certain speed c, where x and y are horizontal coordinates.  A water bug whose distance from the point of impact is p experiences a wave first at a time t=p/c but thereafter continues to feel ripples.  These ripples die down, like t (to the) -1 but theroretically continue forever.  (Physically, when the ripples become small enough, the wave equation is not really valid anymore as other physical effects begin to dominate.)
				One can speculate what it would have been like to live in Flatland, a two dimensional world.  Communication would be difficult because light and sound waves would not propogate sharply.  It would be a noisy world!  It turns out that if you solve the wave equation in N dimensions, that signals propogate sharply (i.e Huygens's principle is valid) only for dimensions N = 3,5,7,.......Thus three is the "best of all possible"dimension, the smallest dimension in which signals propogate sharply!

			This concept is interesting because we can imagine a wave in lineland - it comes and goes and that is it - we can chart sound as it waves through the air on computers and yet this passage tells us that in two dimensions (Flatland) the waves will continue forever.  My question is this;
		What would waves look like or appear to be in the fourth dimension and will they continue forever like those in Flatland?