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Equation of motion/wave equation: (Eq. ) -

This equation comes directly from inserting our result for the y-component of the tension into the result for the segment response. To understand it physically, we can rearrange it as . This states that the acceleration of each segment is directly proportional to the tautness of the string (which makes sense because there should be more acceleration when there are stronger tension forces), is inversely proportional to the mass density of the string (again, sensible because with more mass density, each segment is heavier and accelerates less easily) and is directly proportional to the curvature in the string. The reason why the amount of curvature determines the acceleration is that if there is no curvature (i.e., the string is straight), then the y-components of the tension on either end will be the same and will cancel, leaving no net force. The greater the curvature, the greater the difference in the y-components on either end of a segment, and thus the greater the acceleration.