Movement in Taekwon-do is dynamic and difficult to describe, we have;

• Normal motion
• Slow motion
• Fast motion
• Continuous motion
• Connecting motion

Described in the encyclopedia are also quick motion, releasing motion and consecutive kick.

Sine Wave motion incorporates all the motions mentioned above depending on the movement we are to make.

Normal motion:
One full sine wave is completed during each breath. Saju-Jirugi

Slow motion:
Is performed slowly with slow breathing. This is used to emphasize an important movement and to check balance and control. There is one (slow) movement, one sine wave, in one breath.  Joong-Gun

Fast motion:
Urgent and aggressive, two movements are performed consecutively at fast speed, with two sine wave and two breaths. Fast motion, mostly always attacks,  mainly two punches. Do-San

Continuous motion:
Two sine waves during one breath, as part of two consecutive movements, link the movements together with no pause between the end of one movement and the start of the next. Breath in once then out in a continuous flow of air but emphasizing each movement. Continuous movements always start with a block. Dan-Gun

Connecting motion:
Two movements are performed in one sine wave and one breath, Connecting motion is always with two movements using opposite arms. Yul-Gok.

Quick motion: is used for single movements as opposed to fast motion, which describes how two or more movements should be performed together.

Releasing motion: is a releasing technique

Consecutive kick: do not put your foot on the ground after the first kick

Ref:
Sinewave Study by Master Paul McPhail
Sine Wave motion by  Brian Malm