The strings of a guitar (Fig. 8.26) are made of music wire with diameter \(0.05 \mathrm{~mm}\), weight density \(76.5 \mathrm{kN} / \mathrm{m}^{3}\), and Young's modulus \(207 \mathrm{GPa}\). If the lengths of two of the strings are given by \(0.60 \mathrm{~m}\) and \(0.65 \mathrm{~m}\), determine the fundamental natural frequencies of the strings if the tension in each string is \(5 \times 10^{4} \mathrm{~N}\).

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FIGURE 8.26 Guitar.