You already made a mistake: giving them the first number. Don't compound it now by backing down from the number you've given.
There's only one right answer to the question of what your salary requirements are, and it's "what are you offering?" You'd better believe that if a company is searching for someone to fill a position, they knew exactly what it's worth to them before they ever posted the job offer, but all too often, potential employers will attempt to leverage information asymmetry against candidates. Afterall, if they can get you to name a number below the value of the job, you've just saved them the work of having to negotiate for it!
Now that you've sent it, though, if you're not hearing back from them, it means exactly the same thing as not hearing back from any other job prospect: they're not getting back to you. Nothing more, nothing less. Just treat it as any other prospect that didn't pan out, and keep on actively looking elsewhere. And next time someone asks about your salary requirements, just laugh and say "come on, you know there's only one answer to that question: what are you offering?" Try and present it as an "I see what you did there" moment; don't be hostile about it but make it clear that they're not going to get away with that.
Then when they give you a value, you're the one with the ability to negotiate. If it's better than you expected, just say "that sounds great!" and save yourself the trouble. If it could be better, you can say "oh? I was kinda hoping for something more like X," and they'll most likely find it reasonable. (Remember, they're trying to pay less than what the position is worth.) And if it's way too low, you say something like "are you sure? The [post/ad/recruiter/whatever] said the position was for [this level of qualifications,] and in my experience the going rate for that is more like X. I just want to make sure I'm not applying for the wrong thing here." (This will generally result in an abrupt end to the application process, but that's not a bad thing. You don't want to work at a place where the company culture has no problem with screwing its employees over.)
It's an important thing to remember when job hunting: never volunteer information that can be used to negotiate against you. No, you aren't going to give them your salary requirements. No, you definitely aren't going to tell them your current salary or salary history! No, you don't currently have any serious offers from anyone else. (This isn't even a lie; the only offer you should take seriously is a formal job offer after you have accepted it.)
For the moment, with this place that's not getting back to you... just keep looking. And remember not to make the same mistake next time.