Initially, the frequency of B ($f_B$) could be 512 ± 5, so either 507 Hz or 503 Hz. Filing a tuning fork increases its frequency. If $f_B$ was 503 Hz, filing would increase it further, increasing the beat frequency. If $f_B$ was 507 Hz, filing increases its frequency towards 512, which would decrease the beat frequency. The question seems flawed; assuming "loaded with wax" instead of "filed" would make 503 Hz the answer. Given the options, and assuming a typo from "loaded" to "filed", 507 Hz is the intended answer if "filing" meant moving away from 512. Let's assume "B is loaded" (frequency decreases). If it was 507, loading would decrease it further, increasing beats. If it was 503, loading would decrease it to 512-5=507, giving 5 beats. No, that's not right. The hint is missing. Sticking to the text: if B is 507, filing increases it. If B is 503, filing increases it. There must be an error in the question. However, if we assume the new frequency is 512+5=503, and it increased from original, the original must have been 507Hz. This is a common pattern for such questions.