Active electric motor for on specify voltage
It seems you want to turn on a 9 V motor from a 0-1 V control signal.

One way is to use a NPN low side switch:



You didn't say how much current the motor draws, but let's say 500 mA, and that the transistor can be counted on to have a gain of 50.  That means you need at least 10 mA base current.  Figure the worst case B-E voltage drop is 750 mV, which leaves 250 mV across R1.  (250 mV)/(10 mA) = 25 &Omega;, which is the maximum allowed base resistor. 20 &Omega; might be a good value in that case.

Added:

You have now changed the question so that you want a control signal threshold to be 500 mV to decide whether the motor should be on or not.

This can no longer be done with the circuit above, which was for the spec of 1 V control signal to turn on the motor.  With such a low threshold, you should use a comparator, which can then drive a transistor to turn on the motor.  You will have to provide the 500 mV threshold voltage to one input of the comparator, and the control signal to the other input.  If the 9 V supply is stable, you can derive the 500 mV reference from it with a resistor divider.  Otherwise, you can use the 9 V supply to power a regulated reference that ultimately produces 500 mV.

As for controlling the motor from a 3.5 mm jack, you can use any connector you like.  If you want to drive the motor from a audio signal above some amplitude, then that is again a totally different question.  I'm not going to keep chasing a changing spec.