How long would it take for inbreeding to become a problem within a certain population?

I'm working with a city that has cut itself off from the surrounding area. There may be as many as 10,000 people within it, or as few as 1000. I'm trying to be as realistic as possible. How long would it take for inbreeding to present problems, ie genetic diseases, or mental health issues? This will give me an idea how many people live in the city and how long it has been in existence. Let's assume that the city was founded by nine families that were quite diverse in their genetic code.

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How long would it take for inbreeding to become a problem within a certain population?

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