Final answer:
When two tuning forks with slightly different frequencies are struck simultaneously, they produce beats. By comparing the beat frequencies produced by the unknown tuning fork with two known tuning forks, we can deduce the frequency of the unknown tuning fork. Therefore, the correct option is A.
Step-by-step explanation:
To find the frequency of the unknown tuning fork, we can use the concept of beat frequency. When two tuning forks with slightly different frequencies are struck simultaneously, they produce beats. The beat frequency is equal to the absolute difference between the frequencies of the two tuning forks.
In this case, when tuning fork A with a frequency of 256 Hz produces beats with the unknown tuning fork, and the same unknown tuning fork produces double the beats per second with tuning fork B with a frequency of 262 Hz, we can deduce that the frequency of the unknown tuning fork is between 256 Hz and 262 Hz.
Since option A is within this range, the frequency of the unknown tuning fork is option A. 262 Hz.