Question

Two interfering sinusoidal waves are described by the wavefunctions: y1 = A sin(kx-ωt) and y2 = A sin(kx-ωt+φ). If φ cannot exceed π/2 (0 ≤ φ ≤ π/2), then which of the following is true about the resultant amplitude Ares?

Answer 1

$y_1=A\sin(kx-\omega t),$

$y_2=A\sin(k x-\omega t+\varphi),$

$y=y_1+y_2=2A\cos\frac{\varphi}2\sin(k x-\omega t+\frac{\varphi}2),$

$A_{res}=2A\cos\frac{\varphi}2.$