(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)?