Schrödinger's Cormorant

(4-5) We're considering case 2: two sine waves that are identical except that this time they are exactly out of phase, meaning that the peaks in one line up with the troughs in the other.

① Looking at the y = sin(x) graph (below), by how many radians must another sinusoid be shifted to make it exactly out of phase with the original? With this in mind, and recalling from section 4.3 how to incorporate a phase shift into the equation for a sinusoidal wave:

write down the equation for the phase-shifted wave which will travel excatly out of phase with our original wave, which was defined by y1 = Asin(2π(x-vt)/λ) .

② write down the expression for (y1 + y2) as a function of x for the superposed, out-of-phase waves.

③ figure out what this expression adds up to.

You could do this by visual inspection of the curves:

Alternatively, you might enjoy using your trigonometric identities: if you have come across these, you know you can use the expression:

sin(a-b) = sin(a)cos(b) – cos(a)sin(b).

If this is new to you, it’s worth following up on these trigonometric identities, as we’ll be using them again.

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