If police knock on your door, you hear them, and then they hear sounds suggesting evidence is being destroyed, they can enter without a warrant. The fact that their presence caused your reaction does not invalidate the search.
The exigent circumstances exception to the warrant requirement applies even when police create the exigency by knocking and announcing themselves, as long as they do not violate the Fourth Amendment in doing so.
Police who knock can enter without a warrant if they believe evidence is being destroyed. Don't destroy evidence when police knock.
LEGAL DISCLAIMER: Case summaries are for educational purposes only and do not constitute legal advice. Consult a licensed attorney for advice specific to your situation.