Does my model aircraft propeller beat the sound barrier? I fly model aircraft. Recently I changed from a "1300kv" motor to a "1500kv" motor. The difference is in speed; the 1300kv can go about 16,400rpm full-throttle and with a fully charged battery and the 1500kv can go nearly 19,000rpm. (This is no load speed, but the prop adds very little load when the aircraft is not flying.)
I noticed that when I increased the throttle beyond about 75% the motor and propeller became incredibly loud. Below that they were loud, but no where near as much.
So I did some ballpark calculations. I'm using a 7x3.5" propeller - which means it has a 7" diameter and 3.5" pitch. In this case we are only interested in diameter. 7" diameter means 3.5" radius, or 8.86 cm. Doing 19,000 rpm means than I'm doing about 317 rps. According to 2 * pi * r the circumfrence of the prop's tip is 55.64 cm. Plug this into 317 rps and we get 17,638 cm/s or 176.4 m/s. Which is about half the speed of sound.
Although this is not actually the speed of sound it's very close to it, and much higher than I expected. So what does that mean? I figure that although the propeller itself isn't traveling faster than the speed of sound, the air it pushes out of the way is. My physics teacher showed that if you take a metre stick and swing it through the air (avoiding hitting anyone) it makes a wooshing sound - the air is moving faster than the ruler was. So the prop is pushing the air away faster than this and causing this very loud noise. 
Is my reasoning correct? Is my prop breaking the sound barrier?!
 A: In general yes, you may have supersonic flow in some areas.
But prop is subsonic, and should work fine till 0.9mach (~300 m/s) if it have optimal shape for that speed (some planes even had variable prop's angle of attack to get this for all speeds).
So, in your case you must have excessive noise due to turbulent air flow due to non-optimal prop shape. When flow goes from laminar to turbulent - you should hear significant increase in noise.
A: It is important to note that if you bench test the prop. At a determined speed the prop will not be able to get clean air the air expelled from the back will start to flow to the front due to the very thin air in the front of the prop. This will cause as @BarsMonster states for the air to become turbulent. If the plane is flaying the prop gets clean air all the time and it should not make the noise. If it does the shock wave at the tips of the blade will cause it to actually slow down and speed up again. the plane in flight will make a strange off and on loud humming. Props are designed to not go supersonic at the tips. The rpm and diameter must be just right. This is why on turbo props the blades have flat ends and a shorter diameter. 
A: Just a related comment. When we first started flying Ultralight Aircraft in the 70s, they all had two cycle engines with the props coupled directly to the engine shaft. They had short wooden props and were loud as hell. RPMs on these engines was in the 5 to 7 thousand range. I was told that to use longer props would cause the tips to exceed the speed of sound and they would fail catastrophically.  In the early 80s a reduction gearing was developed and universally adopted because it allowed for longer slower turning props.
