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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 ff of a wave is related to its period of oscillation TT as follows:

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


2- The phenomenon of beating\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:

fbeat=f1f2\begin{gather*} f_{\text{beat}}=|f_1-f_2|\tag{2} \end{gather*}

where f1f_1 and f2f_2 are the frequencies of the individual waves.

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