Engine - 400cc Single cylinder 4 stroke on motorcycle.
Question. What is the design purpose of an intake plenum with "snorkel" inlet ?
My feelings :
a) Noise reduction. ( It is noisy with no airbox - not a suck noise, more like the exhaust sound )
b) Possible Tuning, smoother running ?
I'm not concerned about noise. If so should I remove the airbox for better running? ( I will rejet ( Mikuni CV carb ) to suit the increased air flow I'd expect.)

Any engine will make the most horsepower by allowing it to intake the most volume of air, given that the proper fuel/air ratio is maintained for proper combustion by rejetting the carb or remapping the fuel injection.

  Unless the air box and snorkel are designed to provide a ram effect at speed like some of the newer bikes, removing the air box will eliminate restriction before the carb and potentially give more power.

  There are other factors to consider. Many times the intake tract at the entry to the carb is rough and a better transition for the air is benneficial. Because of this removing the air box will sometimes net less airflow. A velocity stack is a good solution to solve this problem. Another thing to consider is an air filter. Unless this is clean enviroment (?Safety valves) racing engine or an experiment you need air filtration.  There are all kinds of "cone" filters out there to solve that issue.

Tuned length and a bell mouthed entry into the duct, or stack or trumpet or velocity stack or ram tube or whatever you want to call it, are very good at promoting airflow between the plenum and the valve, but tuned length into the plenum is in my opinion is a waste of time.  

Snorkels in my opinion are for sound dampening and maybe cold air induction only. Reducing the temperature of the air being drawn into the motor most certainly is an effective way to increase power.

The shape of the filter is not significant. The pore size and surface area are what counts.

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