A guitar string produces 3 beats/s when sounded with a 352-hz tuning fork and 8 beats/s when sounded with a 357-hz tuning fork.

Explanation:

The fluctuating sound heard when two objects vibrate with different frequencies is called beats. It is given that guitar string produces 3 beats/s when sounded with a 352 Hz tuning fork and 8 beats/s when sounded with a 357 Hz tuning fork.

It is assumed to find the vibrational frequency of the string.

For 3 beats/s, beat frequency can be :

352 - 3 or 352 + 3 = 349 Hz or 355 Hz

For 8 beats/s, beat frequency can be :

357 - 8 or 357 + 8 = 349 Hz or 365 Hz

It means that the vibrational frequency is 349 Hz.