I started Taekwondo in the 1960’s, studying from an ROK (Republic of Korea) Marine. The sine wave was never mentioned and I never saw it used. In fact, we were taught that, while moving, the belt knot should move in the direction of the movement but should not move up or down.
I purchased the first edition of General Choi Hong Hi’s book on Taekwondo in 1970 and it does not mention the sine wave. In face, none of the early books by Taekwondo masters, such as Richard Chun, Joon Ree, etc., ever mentioned a sine wave movement. Apparently Choi and his instructors came up with the sine wave, heel drop, and knee snap concepts on their own.
The World Taekwondo Federation does not use the sine wave and many, if not most, of the other Taekwondo associations around the world do not use it. The sine wave is not a natural movement, it adds unnecessary movements to any technique, and as such, it follows that it must slow a technique, and it does not add any effective power to a technique. Runners don’t bob up and down and we don’t bob up and down when we walk. Animals don’t bob either. For example, when a cat or dog is moving, its spine stays in straight, level line.