Question

Two of the three tuning forks have known frequencies. When a 510 Hz. fork and the unknown fork are struck together, four beats per second are heard. When a 505 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?

Answer 1

4 Hz is the difference between 510 and the unknown. 
Therefore the unknown is either 514 or 506. 

If 505 and 506 were struck together, the diff would be 1 Hz 
If 505 and 514 were struck toghether, the diff would be 9 Hz which would be difficult to count accurately, 

Therefore the unknown is 514