According to the knock and announce rule, what is a reasonable amount of time to wait before an officer may break and enter?
There is no hard-and-fast rule about what is reasonable. It can vary with the situation involved.
One rule that has been articulated was set out in US v. Banks. In this case, the Supreme Court ruled that 15 to 20 seconds was a sufficient amount of time to wait before forcing an entry into an apartment. In this case, the reasoning was that the officers had a warrant to search for cocaine and waiting any longer than that to break in would have allowed the suspect to have time to flush the cocaine or otherwise get rid of it. Presumably, had the officers been looking for something less easy to get rid of, a longer wait would have been reasonable.
So, there is no concrete rule, but in some cases as little as 15 seconds is acceptable.