Frequencies for a standing wave on a string (13-19)

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Question

\(n\)th possible frequency of a standing wave on a string held at both ends
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Review

By combining Equations 13-2 and 13-10, we get the following relationship between the frequency \(f\) and wavelength \(\lambda\) of a wave on a string:

\(f\lambda = \sqrt{\frac{F}{\mu}}\) or \(f = \frac{1}{\lambda}\sqrt{\frac{F}{\mu}}\)

To make this specific to \(\textit{standing}\) waves on a string, we use the relation \(L = n\lambda/2\) from Equation 13-18, which we can rewrite as \((1\ /\ \lambda) = n\ /\ (2L)\). Substituting this into the above equation, we get: