Do smaller birds need to flap their wings faster?

When comparing two of my reference videos, I found that a smaller bird had a faster flight cycle and so wanted to find out if this is common and why.

http://wiki.answers.com/Q/Why_do_small_birds_flap_their_wings_faster_than_large_birds_in_flight

It is a combination of factors, though I'm not sure if only one is more important than another...however, they all contribute into the same end product and one common factor: smaller birds are birds of prey.
1) Wing span: smaller the bird, shorter the wing span from wing tip to wing tip. This makes it necessary to flap more frequently to keep the lift required to compensate for their weight.
2) Environment: small birds need to hide from predators, therefore they live in mostly forested or grassy places to find safety in the form of shelter. This also makes it necessary for them to be able to make sudden maneuvers and sharp turns - which a larger wingspan would hinder.
3) Escape: needing to flee suddenly requires one to be able to get lift with little momentum...if they were larger (heavier) and had a greater wing span this would add too much bulk and slow them down.