"Which gives the transverse acceleration of an element on a string as a wave moves along an x axis along the string?"

the second derivative of y with respect to time gives the transverse acceleration of an element on a string as a wave moves along an x axis along the string

Explanation:

This is because the transverse wave movement of particles take place in direction 90° to direction of movement of the wave (x) itself, so second derivative of y with respect to time (t)is what will be required

the independent variable, or the one that is intentionally manipulated is the speed.

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