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Typically 3600 rpm for 60 hz production.
Above answer is not very specific.
The maximum RPM of a turbine generally depends on the maximum diameter of the rotating element. For example a large 240MW gas turbine will run at approximately 3000 RPM whereas a car engine turbo can run at 100 000 RPM and above. The limiting factor is that the blade tip velocity must stay below the speed of sound. On one rotation of a big turbine, the circular distance travelled by the blade tip is much further than the distance travelled by the blade tip of a very small turbine, so the RPM on the bigger turbine must be lower in order to stay below the speed of sound. The speed of sound is variable depending on air density, which is in turn affected by air temperature and altitude, so the blade tip velocities on most units run well below the speed of sound so that they can operate under various ambient conditions.
Many turbine companies experiment with super-sonic blading as the air compressor sections on gas turbines are much more efficient at higher RPM and you could get significantly more output power with better air compression, but (I believe) that all commercial and industrial engines are sub-sonic.
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