Question

What if a wave traveled to the right on a string and its reflection were not inverted? would a standing wave still result? use the trigonometric identity for the sum of the sines of two angles, eq. 2.16, and follow the example presented in eq. 2.1 through eq. 2.5 to answer this question?

Answer 1

Let say the equation of travelling wave is

`y_i = A sin(wt - kx)`

now if the wave is reflected such that it is not inverted after reflection

So the equation of reflected wave will be

`y_r = A sin(wt + kx)`

now we will have

`y = y_i + y_r`

now we will have

`y = Asin(wt - kx) + Asin(wt + kx)`

`y = A[2sin(((wt - kx) +(wt + kx))/(2))cos(((wt - kx) -(wt + kx))/(2))]`

`y = 2Acos(kx)sin(wt)`

so above equation shows the condition of standing waves