16.2 Exercise 2

The wave equation $\frac{\partial^{2} y \left(x , t\right)}{\partial x^{2}} = \frac{1}{v^{2}} \frac{\partial^{2} y \left(x , t\right)}{\partial t^{2}}$ works for any wave of the form $y \left(x , t\right) = f \left(x +- v t\right) .$ In the previous section, we stated that a cosine function could also be used to model a simple harmonic mechanical wave. Check if the wave

is a solution to the wave equation.