Final answer:
The two possible frequencies of the unknown tuning fork, when combined with a tuning fork of 288 Hz to produce a 5 Hz beat frequency, are 283 Hz and 293 Hz.
Step-by-step explanation:
When a scientist hits two tuning forks with one having a known frequency of 288 Hz and the other of unknown frequency, resulting in a beat frequency of 5 Hz, we can calculate the unknown frequency by considering two possibilities. The frequency of the second tuning fork can be either higher or lower than the known frequency, since the beat frequency represents the absolute value of the difference between two frequencies.
Case 1:
The unknown frequency is higher than 288 Hz. Therefore, it would be 288 Hz + 5 Hz = 293 Hz.
Case 2:
The unknown frequency is lower than 288 Hz. Hence, it would be 288 Hz - 5 Hz = 283 Hz.
Thus, the two possible frequencies of the unknown tuning fork are 283 Hz and 293 Hz.