As has been posted before, the air pump has a magnetic clutch that is activated for less than two minutes during a cold engine start. The purpose of the pump is to add air to the engine exhaust when the engine is cold. On a cold engine start, the air/fuel mixture is rather rich and then leans out as the engine heats up. During this minute or so cold start scenario, the pump adds supplemental air into the exhaust header ahead of the catalytic converter. The additional air leans out the exhaust and promotes an after-burn to reduce NOX and SOX (environmentally bad).
Changing the air pump out is an easy task for a DIYer and should take about an hour or so. You should work from below the car and it may be necessary to remove the alternator for access. You can buy a rebuilt pump from Adsit for less than $400. A new pump from the dealer is over $1000!
Usually, the failure of these pumps are in the bearings. If yours is making a rushing sound, you may want to check the discharge hose from the pump..........it may be broken or loose.