Final answer:
The possible frequencies for tuning fork A are 507 Hz or 514 Hz, as these will produce a beat frequency of 5 Hz when combined with the frequency of tuning fork B which is 512 Hz.
Step-by-step explanation:
When two tuning forks A and B produce 5 beats per second and tuning fork B has a frequency of 512 Hz, the possible frequencies for tuning fork A can be determined by either adding or subtracting the beat frequency from fork B's frequency. For option A) 507 Hz, adding 5 Hz gives us 512 Hz, which matches fork B, therefore A could be 507 Hz. For option B) 510 Hz, the difference is 2 Hz, which is not possible as it does not account for the 5 beats per second. For option C) 514 Hz, adding 5 Hz to 509 Hz gives us 514 Hz, which is a possible frequency for fork A. For option D) 517 Hz, the difference does not produce the observed 5 beats per second. Thus, the possible frequencies for tuning fork A are either 507 Hz or 514 Hz.