Question

When solving a 1-Dimensional wave equation using variable separable method, we get the solution if _____________

(a) k is positive

(b) k is negative

(c) k is 0

(d) k can be anything

I got this question in examination.

My doubt is from Solution of PDE by Variable Separation Method topic in portion Applications of Partial Differential Equations of Engineering Mathematics

Answer 1

Correct choice is (b) k is negative

For explanation I would say: Since the given problem is 1-Dimensional wave equation, the solution should be periodic in nature. If k is a positive number, then the solution comes out to be (c7 e^px⁄c+e^-px⁄cc8)(c7 e^pt+e^-ptc8) and if k is positive the solution comes out to be (ccos(px/c) + c’sin(px/c))(c’’cospt + c’’’sinpt). Now, since it should be periodic, the solution is (ccos(px/c) + c’sin(px/c))(c’’cospt + c’’’sinpt).