Step 1: Think physically about how the rotating magnetic field is created rather than starting from the formula. Each cycle of the AC supply pushes the field pattern through one full electrical rotation, so a higher supply frequency f means the field sweeps around faster in a given time.
Step 2: The winding is built with a certain number of magnetic poles P. Increasing the number of poles forces the same electrical cycle to be shared across more pole pairs around the stator, mechanically slowing the field's physical rotation, giving $N_s = \dfrac{120f}{P}$.
Step 3: The rotor always turns slightly slower than the stator field, a difference called slip, and it is the current induced by that slip which produces torque. Current is therefore a consequence of loading, not a cause that changes the field's own rotational speed.
Step 4: Supply voltage sets how strong the magnetic flux and torque can be, but has no role in timing the rotation of the field, since timing is set purely by frequency and pole geometry.
Step 5: So only frequency and pole number set synchronous speed, current and voltage do not, confirming option 1.\[\boxed{N_s = \dfrac{120f}{P}\ \text{depends on frequency and poles only}}\]