Many ITF-based taekwondo practitioners come to notice a difference between different ITF-based organizations with some groups teaching a direct, forceful style and others teaching a more timed, flowing style often referred to as a "sine wave" style. What are the defining characteristics of this "sine wave" approach to ITF hyungs/tuls and how did this style originate?
The "sine wave" terminology is used, in my experience, to refer to a more bouncing method of footwork in forms. A linear, non-size-wave execution of kata, such as this performance from Shotokan, values direct movement, crisp end positions, and minimal up-and-down movement between stances. In contrast, this "sine-wavey" performance from ITF TKD exemplifies the up-and-down, more fluid method that the term refers to. Notice the exaggerated way that the practitioner settles into each step, and the alternating slow-fast cadence of each movement. This is dissimilar from the rather even pace that the Shotokan stylist uses.
I am not familiar with the origin of this style, except to note that preferences regarding the look and feel of kata performance naturally change over time and with different personalities in charge. But the salient differences seem to be: