Step 1: Effective tension (Te) in a belt conveyor is the net pull that the drive pulley must supply to overcome all the resistances along the conveyor, friction at the idlers, flexing of the belt, and lifting the material if the conveyor is inclined.
Step 2: All of these resistances are calculated from the weight of the belt, the weight of the material carried, the friction factor of the idlers, and the conveyor geometry (length and lift). None of these standard resistance formulas contain the belt speed as a variable.
Step 3: What does depend on belt speed is the power required to drive the conveyor, since power = effective tension multiplied by belt speed. So a faster belt needs more power, but not because the effective tension itself changed, it changed because the same tension is now being delivered at a higher speed.
Step 4: Since effective tension is fixed by load and friction and not by how fast the belt travels, the correct statement is that it doesn't depend on belt speed.