A string \( 120 \mathrm{~cm} \) in length and fixed at both ends sustains a standing wave, with ...

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A string \( 120 \mathrm{~cm} \) in length and fixed at both ends sustains a standing wave, with the consecutive points of the string at which the displacement amplitude is equal to \( 3.5 \mathrm{~mm} \) (not maximum) being separated by \( 15.0 \mathrm{~cm} \). The maximum displacement amplitude is \( 3.5 \mathrm{x}^{1 / 2} \) in \( \mathrm{mm} \). Then find \( \mathrm{x} \). To which overtone do these oscillations correspond?
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