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I am unclear that when a stretched string oscillates , does it oscillate in its fundamental or in its overtones. And I want to know whether there are any instances where a stretched string oscillate in one of its overtones as its natural frequency?

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A string played on a musical instrument will oscillate in a mix of its harmonics, although its fundamental frequency will usually be the loudest single component. The exact mix of harmonics will depend on whether the string is plucked, bowed or struck with a hammer; the place on the string where it is plucked, bowed or struck; and the force with which it is plucked, bowed or struck (the "velocity"). In addition, the body of the instrument (known as its "sound box") will resonate with certain frequencies and amplify them, changing the quality or "timbre" of the note.

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