Unless you have failed for the 3rd time, there is no wait period at all, you can schedule your next exam immediately. This is called reexamination, so you won't have to re-apply for PMP another time, you just schedule the exam.
However, if its the third time you've failed the exam, then you have to wait for a year after your last exam, until you're eligible to re-apply for PMP. (Source: The PMP Handbook, page 28)
Note that even if you failed for the first time, you can still apply for another PMI credential immediately (including CAPM, PgMP, PMI-RMP...).