One tuning fork vibrates at 440 Hz, while a second tuning fork vibrates at an unknown frequency. When both tuning forks are sounded simultaneously, you hear a tone that rises and falls three times per second. What is the frequency of the second tuning fork?

On sounding two tuning forks together, we hear beats which is heard at a rate equal to difference of frequencies of tuning forks.

In the present case too, beat is heard.

Frequency of beat heard = 3

The frequency of second tuning fork must be higher by 3 or lower by 3

So the possible frequencies of vibration of unknown tuning fork = 440 + 3 or 440 - 3

443 Hz

or, 437 Hz.

443 Or 437 is the answer.