Question

The general solution of one dimensional wave equation \[ \frac{\partial^2v}{\partial t^2} = c^2 \frac{\partial^2v}{\partial x^2} \] is \(u(x,t)=\)

• A. \(f(x+ct)\,g(x-ct)\)
• B. \(f(x+ct)+g(x-ct)\)
• C. \(f(x-ct)+g(x-ct)\)
• D. \(f(x+ct)+g(x+ct)\)

Hint:

D'Alembert's solution is \[ \boxed{ u(x,t) = f(x-ct) + g(x+ct), } \] representing two waves travelling in opposite directions with speed \(c\).

Answer 1

The Correct Option is B