Wave is a disturbance in a medium, due to this disturbance the particles in the medium oscillate. Due to this oscillation we say that the wave is sinusoidal because the motion of the particle is periodic. So we REPRESENT the motion in sine wave.
Periodic motion can be represented by sine graphs. So if instead of representing in sine graph can we represent it as square (instead of curves) periodic graph ?.
Ps: also please confirm if the first paragraph is correct (kind of confused in that too).