Hi Bernie,

 

Certainly not an expert here, but my understanding is that at the
atmospheric altitudes we fly at that air temperature is the dominant factor
governing the speed of sound, not density, not humidity, not pressure - at
least not significantly.  But, then my interpretation could be wrong.

 

Forward speed of the aircraft is a factor to consider as others have pointed
out.  I know that compressibility effects start long before a shock wave is
created at the speed of sound, the latter  which you certainly want to
avoid.  I imagine that the shape of the object probably has a lot to do with
it not to mention that you have the radial speed component and the
horizontal speed component all interacting.  Airflow around the prop is
probably being affected long before the speed of sound - but, how long I
simply don't know.  I would suggest research on the internet on the topic.