Why does a running fan produces some sound? We see that a running fan produces some "humming" sound - "The sound of air". What kind of sound it is? 
Why does a running fan produce some sound? 
 A: As a fan blade moves through the air, it pushes a pulse of air away from the fan and towards you. You perceive this as a single pulse of "whump" sound. 
For a slow-turning three-bladed fan, three pulses of whump sound are produced for each motor shaft revolution, and you hear whump whump whump.
Now you speed the fan all the way up and the individual whumps blend into a continuous wave that is more or less a sine wave at a frequency equal to the number of blade passages per second. 
Superimposed on the blade passage noise is a steady roar or hiss caused by turbulent motions of the air flow as it squeezes through the protective grill on the fan housing. 
If you make the fan blades wide enough so the trailing edge of each one overlaps the leading edge of the next one, you can greatly reduce the blade passage noise and all you will hear will be the hiss. 
Because of the greater surface area of an overlapping fan disc, it will experience more friction with the air and therefore exhibit lower efficiency than a (far noisier) fan with slender blades that have no overlap. 
