Question

A guitar string produces 3 beats/s when sounded with a 352 Hz tuning fork and 8 beat/s when sounded with a 357 Hz tuning fork. What is the vibrational frequency (in Hz) of the string

Answer 1

349 Hz

Step-by-step explanation:

We are told that the guitar string produces 3 beats/s when sounded with a 352 Hz tuning fork and 8 beat/s when sounded with a 357 Hz tuning fork.

This means that for the 352 Hz tuning fork, the vibrational frequency is;

f = 352 ± 3

f = (352 + 3) or (352 - 3)

f = 355 Hz or 349Hz

For the 357 Hz tuning fork, the vibrational frequency is;

f = 357 ± 8

f = (357 + 8) or (357 - 8)

f = 365 Hz or 349 Hz

In both cases, 349 Hz is common;

Thus, the vibrational frequency of the string = 349 Hz