Chapter 12, Problem 42P

To determine

The vibrational frequency of a guitar string.

Answer to Problem 42P

  $f=346\text{ Hz}$

Explanation of Solution

Given:

String produces   = 4 beats/s, and sounded with $f=350\text{ Hz}\text{.}$

Tuning fork  = 9 beats/s, and sounded with $f=355\text{ Hz}\text{.}$

Formula used:

Beats/s = [350 − f ]and [355 − f ].

Calculation: 

A guitar string is sounded at the same time as a tuning fork.

4 beats/s = [350- f ],

  $f=\text{ 3}50-4=346Hz.$

9 beats/s = [355- f ],

  $f=\text{ 3}55-9=346Hz.$

Therefore, the vibrational frequency of the sound is 346 Hz.

Conclusion: 

The vibrational frequency of a guitar string is 346 Hz.