(4-9)  We’ll take a simple example of a superposition of two waves with different wavelengths, travelling in opposite directions (as shown by the opposite signs of the vt term):

                                                                  y  = sin(x-vt)  +  sin(2(x+vt))

This function is a wave , as you can see in the graphs below:  as the time increases, the waveform is translated progressively to the right but it retains its form:

So, if our general wave equation is valid, it should work for this function.

①   find the partial derivatives, ∂y/∂x and ∂y/∂t.


②  Is this wave superposition consistent with the first order wave equation we have derived (equation IV-4)?