How do I know if my air admitance valve is faulty

What is causing you to ask the question? One way to check is to tie a light plastic bag around the AAV so it is tightly sealed. Then, drain the device the AAV is connected to. If it is working properly, the bag should stay still as water is running down. Quickly shut the drain and you should see the bag contract as the air is pulled from it. You can also use smoke tubes used tor checking air flow. You should see smoke being pulled into the AAV as the water is running by. Smoke should not show any air emanating from the valve. Finally you can use the sniff test. You should not smell any sewer gas when an AAV is functioning properly.

Outstanding answer Brain.
I was going to ask if the OP heard any gurgles as the sink drained but yours id much better, Cheers. Tom