Very few questions can not be answered by searching the web, and if repeat questions are not allowed. The site will slowly move from a forum to a data base. Is the site concerned about this?
It was never a forum to begin. The goal of the site is to provide high quality Q&A from experts in the field. If we've answered every question, then mission accomplished.
But since science progresses, we will never be able to keep up with the questions at the leading edge of it. If science stops progressing and there is nothing new in the broad areas covered by the site, then there's a lot more to worry about than the future of the site here.
In other words, I'm not concerned about it.
And maybe to clear up another point of concern -- yes, most things can be found by using your favorite search engine. But unless the first hit, with the most comprehensive and accessible approach to answer your question, is not this site, then there's still work to be done. If you can get your answer by stitching together a few Wikipedia articles and some Yahoo Ask questions, cool. But that doesn't mean that question (and the resulting researched answer) shouldn't appear here too, as a single, authoritative source.
I think that a certain density of repeat questions is a good thing, and should be supported.
The reason I think this is that repeat questions encourage new answers, and the answers may not be repeats. It's tempting to say 'but physics is a hard science, there's only ever one right answer', but I think that's not true: new answers can present and encourage new ways of thinking about an existing area, and that's a good thing. This is why, for instance, new textbooks on old areas of physics can still be interesting.
One answer to this is 'well, you can just add new answers to old questions'. However, if old questions already have accepted answers then any new answer is extremely unlikely to be accepted. So anyone interested in reputation is thus going to be put off by that. Of course, one could then argue that, well, you should not be interested in reputation: that's nice in theory but, in fact, people are interested in reputation and the whole site is predicated on that. Thus not allowing duplicates is likely to actively suppress new answers.
So I think a certain, not too high, ratio of repeat questions should be allowed.
Of course, this is just my opinion.