Most solenoids can't open and close that quickly. Assume the solenoid has to move 1mm from fully-closed to fully-open. And it has to do this 4800 times per second. Thats 4.8 metres per second, or 17kph. That doesn't seem exceptionally fast.

But it has to go from 4.8m/s 'forward' to 4.8m/s 'backwards' in half of one 4800th of a second. That's an acceleration of more than 9000 times the force of gravity.

Now assume the moving mass of the solenoid is 2 grams. The force required to accelerate it is 184N, equivalent to about 18kg. I guess you have to assume that the outer part of the solenoid is capable of applying that kind of force to the little 2g plunger inside it without smashing it flat.

Work = force X distance, so there's 0.18 joules used to move the moving element. Do that 4800 times down and 4800 times up in one second and you get 1.7 KILOWATTS of power. Assuming it's a 12V solenoid (very common) that needs 147 AMPS of current.

Yes, you will need transistors to switch 147 amps.

Would you like to ask the question a different way? What are you really doing?