Two of the three tuning forks have known frequencies. when a 610 hz fork and the unknown fork are struck together, four beats per second are heard. when a 605 hz fork is struck with the unknown fork, beats are produced that are too numerous to count accurately. what is the frequency of the unknown fork?
614
606

-- In combination with 610 Hz, the beat frequency is 4 Hz.

So the unknown frequency is either (610+4) = 614 Hz
or else (610-4) = 606 Hz.

In combination with 605 Hz, the beat frequency will be
either (614-605) = 9 Hz or else (606-605) = 1 Hz.

-- In actuality, when combined with the 605 Hz, the beat
frequency is too high to count accurately.  That must be
the 9 Hz rather than the 1 Hz.

So the unknown is (605+9) = 614 Hz.
 

None. nothing. zero. zilch.