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Question: "How is the wave equation derived?

This is the question.

Here is my answer. I am trying to ensure that it is correct.

"To derive wave equation, we apply Newton's law to an elastic string, concluding that small amplitude transverse vibrations of the string obey the wave equation"

(2) Then What are the three components necessary for this equation?

(3) What does each mean?

My question: Are the three components referred to in question 2, Newton's 2nd law, constitutive relations and the liberal application of linearization?

Please help clarify