Chapter 20: Problem 50

Question:        A tuning fork of unknown frequency makes $\nu_{\rm beat} = 3\ {\rm Hz}$ with a standard tuning fork of frequency $\nu_0 = 384\ {\rm Hz}$. The beat frequency decreases when a small piece of wax is placed on the prong of the first fork. What is the frequency of this fork.

Solution:        

A beat frequency of $\nu_{\rm beat} = 3\ {\rm Hz}$ indicates that the fork has possible frequencies $\nu = \nu_0\pm 3$ which is either $387\ {\rm Hz}$ or $381\ {\rm Hz}$. The addition of the wax will reduce the frequency of the fork, and that the beat frequency decreases, we conclude that $\nu = 387\ {\rm Hz}$.