Question

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

Answer 1

-- 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.