Which of the following is a solution to the wave equation, $\frac { \partial ^ { 2 } y } { \partial x ^ { 2 } } = \frac { 1 } { v ^ { 2 } } \frac { \partial ^ { 2 } y } { \partial t ^ { 2 } }$ ? A) $\frac { e ^ { - x } } { x } \sin x$ B)(cos kx)(sin $ \omega $t) C)e ^- ^x sin $ \omega $t D)e ^- ^x sin (kx - $ \omega $t) E)e ^- ^x cos t

Question

Quizplus · Accepted Answer

The wave equation is given by:

∂²u/∂t² = v² ∂²u/∂x²

The solution to this equation is given by a function that satisfies the following conditions:

u(x, t) = f(x-vt) + g(x+vt)

The solution given in choice B is in this form and satisfies the wave equation. The other options may look like solutions to a wave equation, but they do not match the form given above or do not satisfy the equation. Therefore, B is the best choice.

Which of the Following Is a Solution to the Wave ∂2y∂x2=1v2∂2y∂t2\frac { \partial ^ { 2 } y } { \partial x ^ { 2 } } = \frac { 1 } { v ^ { 2 } } \frac { \partial ^ { 2 } y } { \partial t ^ { 2 } }∂x2∂2y​=v21​∂t2∂2y​

Which of the Following Is a Solution to the Wave $\frac { \partial ^ { 2 } y } { \partial x ^ { 2 } } = \frac { 1 } { v ^ { 2 } } \frac { \partial ^ { 2 } y } { \partial t ^ { 2 } }$