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String Tension

The tension of a vibrating string is the force $ F$ used to stretch it. It is therefore directed along the axis of the string. A force $ F$ must be applied at the endpoint on the right, and a force $ -F$ is applied at the endpoint on the left. Each point interior to the string is pulled equally to the left and right, i.e., the net force on an interior point is $ F + (-F) = 0$. (A nonzero force on a massless point would produce an infinite acceleration.)

If the cross-sectional area of the string is $ S$, then the tension is given by the stress on the string times $ S$.
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Non-Stiff String
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Young's Modulus