Quantifying metal grill effect on sound?

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Some thoughts that pertain to the LF realm...

When you obstruct airflow in front of the cone that adds to the restoring force of the air trapped between the grill and the cone making the suspension stiffer (k goes up).

Since Cms is the inverse of k, Cms decreases due to the added stiffness.
Then the woofer's Vas is lowered as well (Vas = air density x speed of sound x Sd x Cms).

The added stiffness serves to damp the motion of the cone. You will lose some efficiency in the lowest frequencies but get slightly improved transient response for tighter bass and less ringing. All this can be safely assumed for a sealed subwoofer.

If this is a bass reflex system in question then it's hard to accurately predict the same effects since they are so dependent on the boundary conditions that exist between the port exit and the grill. I imagine the grill can alter the tuning of the port - further changing the damping quality of the system which effects excursion. I also imagine the grill adds to port distortion at high air velocities due to the turbulence it would cause.

It's challenging to know the sum of the effects with a low margin of error and high confidence level since this is a lumped approach but perhaps a more distributed system exists for knowing with higher certainty.
 
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