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# A piano tuner hears a beat every 2.00 s when listening to a 264.0-Hz tuning fork and a single piano string. What are the two possible frequencies of the string?

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### 1 Concepts and Principles

1- The frequency $f$ of a wave is related to its period of oscillation $T$ as follows:

$\begin{gather*} f=\dfrac{1}{T}\tag{1} \end{gather*}$

2- The phenomenon of $\textbf{beating}$ is the periodic variation in intensity at a given point due to the superposition of two waves having slightly different frequencies. The beat frequency is:

$\begin{gather*} f_{\text{beat}}=|f_1-f_2|\tag{2} \end{gather*}$

where $f_1$ and $f_2$ are the frequencies of the individual waves.

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