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

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

Correct Answer:

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