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The classical wave equation is derived by applying Newton's second law ($F=ma$) to an infinitesimal element of a string. The net vertical force from tension differences is equated to the element's mass times its vertical acceleration.

Conditions: The string is ideal (knot-free and inextensible), so tension $F_T$ is uniform.; The wave is transverse, so particles move only vertically.; The string disturbance is very small, allowing the small-angle approximation.

The classical wave equation is derived by applying Newton's second law ($F=ma$) to an infinitesimal element of a string. The net vertical force from tension differences is equated to the element's mass times its vertical acceleration.

Conditions: The string is ideal (knot-free and inextensible), so tension $F_T$ is uniform.; The wave is transverse, so particles move only vertically.; The string disturbance is very small, allowing the small-angle approximation.