Does the Engine of an Aircraft run on only one RMP unlike our vehicles' which differs upon changing gears?

Question

Sorry, I mean RPM...

Answer 1

In a turbine engine the engine RPM varys according to the amount of fuel supplied to the combustion chamber of the engine. Basically "a controlled explosion" (quoted from a Navy aircraft engine tester) where the amout of fuel added or taken away speeds or slows down the reaction.
As far as the gears are concerned, the transmission in your car or "gears" as you call them allow us to use the engine's RPMs in different levels. 1st gear for taking off and power, second for acceleration 3rd for less accel and cruise etc... Higher the gear the less the RPMs at a a steady speed.
The gears in a car allow you to move a solid object easier, in an aircraft, the engines move air. Some aircraft like helicopters have transmissions

Answer 2

An aircraft propellor works best in a limited range of speeds which keeps the tip speed close to the speed of sound.

Also, once it has taken off, an aircraft does not change speed much, as the wings are most efficient in quite a narrow speed range.

Some aircraft have constant speed propellors, which actively change their pitch angle so that they absorb the power of the engine without changing speed.
This tends to be turboprop aircraft, where once again the engines operate best in a narrow speed band.

Answer 3

The RPM's for any engine increase with more preasure on the throttle/gas pedal not because of shifting gears.
Airplanes do not have a gear box/transmission like your car. They only have a throttle.
The gears in your car only serve to get the car up to speed. The lower gears inhibit RPM's because of the gear ratio needed to get the car moving.