Some motors have a start up noise, and is normal for that type of motor. My table saw does this. Starts out a loud 60 Hz hum which quickly increases in frequency as the motor spins up, then gets inaudible or washed out by rushing air when full speed is reached. Motors that do this are not really appropriate for residential blowers.
It also possible it's not a normal noise and there is a defect. Very hard to differentiate on the internet. The rhythmic noise sounds like the squirrel cage is slightly hitting something. Perhaps it is misaligned or out of balance. Misalignment or balance issues could also cause the motor to make unusual noises. Something is not right and warrants further investigation. Could very well be minor, or a warning of something that will get worse.
Even if the start up noise were normal, I would be unhappy that a formerly quiet motor was replaced with a noisy one.
Comparing those tables: Note that the speed switch in the circuit you show isn't using L.
A: L+2+3
B: L+1+3
C: L+1 (Maybe this is L+1+2 ???)
D: L+1+2+3
0: No connection (or no connection to anything but L)
1: 2+1 (possibly plus a connection to L)
2: 1+2+3 (possibly plus a connection to L)
3: 2+3 (possibly plus a connection to L)
Making them correspond with each other...
C is obviously equivalent to 0.
D is obviously equivalent to 2.
That leaves us with
A: L+2+3
B: L+1+3
1: 2+1 (possibly plus a connection to L)
3: 2+3 (possibly plus a connection to L)
We can make those match if we relabel the connections. If we just swap the labels on your terminals 3 and 2, then
A is equivalent to 3
B is equivalent to 1
If we renumbered them all (your 2 is their 3, your 3 is their 1, your 1 is their 2), then
A is equivalent to 1
B is equivalent to 3
Pick whichever you prefer; one will switch off-high-medium-low-off, and the other will switch off-low-medium-high-off.
As far as theory goes: I'm not sure either, but let's see what I can do with it.
3 (2->3) appears to be "slow" because power flows through the right half of the bottom coil, and then through the side coil, in series. More resistance, less current flow, less power.
1 (2->1) appears to be "fast" because the left side of the bottom coil, and the side coil, are powered in parallel. Both get the full house-current voltage applied across them rather than the reduced amount of power they got in series.
2 (2->1 and 3) is the tricky one. I am far from certain, so DON'T take my word for it. But I think what's happening here is that, since the middle and right sides of the bottom coil (1 and 3) are now connected to each other, that loop has a current induced in it by the motor's moving magnets, which creates a countering magnetic field, which acts as a magnetic brake to slow the motor... so fast with a bit of braking equals medium. Seems like an odd solution, but if I'm remembering my freshman Physics at all correctly it might actually be a reasonably efficient solution.
You might want to run this by the physics discussion, to get someone with more recent memory of electrodynamics to check and/or correct that last paragraph.
Gopher baroque...
Best Answer
Dead common, but it's more often the circuitry providing the DC voltage to the fan, in my experience.
Not clear what you are powering this from (AC/DC/Voltage...), but the speed control probably consists of some sort of switching circuit, and when there are electronic components that are being switched at audible frequencies, you sometimes get noises you can hear - often quite irritating.