Show that the function is a solution of the wave equation.
-w(x, t) = sin (-10x - 10ct)

Question

Quizplus · Accepted Answer

The wave equation is given by:

∂²w/∂x² = (1/c²) ∂²w/∂t²

Taking the second partial derivative of w(x,t) with respect to x, we get:

∂²w/∂x² = -100 sin(-10x - 10ct)

Taking the second partial derivative of w(x,t) with respect to t, we get:

∂²w/∂t² = -100c² sin(-10x - 10ct)

Now we can substitute these values in the wave equation and see if w(x,t) satisfies it:

-100 sin(-10x - 10ct) = (1/c²) (-100c² sin(-10x - 10ct))
-100 sin(-10x - 10ct) = -100 sin(-10x - 10ct)

Thus, we can see that the function w(x,t) = sin(-10x - 10ct) satisfies the wave equation, and the answer is A.

Show That the Function Is a Solution of the Wave