To tune a guitar string to 329 Hz, you compare its frequency with a 329-Hz tuning fork

The detailed solution is explained below:

Step-by-step explanation

The frequency of the guitar string is inversely proportional to the beat frequency, it is given as the difference of the frequencies, the calculation is shown below:

??f1?−f2??=fbeat??329−f2??=5329−f2?=−5329−f2?=5f2?=334,324??

From the above calculation we can see that two values are possible for the initial frequency, the calculation for the final frequency is shown below:

??f2?−f3??=fbeat??334−f3??=3f3?>334334−f3?=−3f3?=337Hz?334−f3??=3334−f3?=−3f3?=337Hz324−f3?=−3f3?=327Hz??

Thus, we can see that two values of the final frequency is also possible for the given initial frequencies.

(334,337),(324,327)