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?

A√2 ≤ Ares ≤ 2A

A√2 ≤ Ares ≤ 2A√2

A ≤ Ares ≤ 2A

A ≤ Ares ≤ A√2

Answer 1

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

$A\sqrt2 ≤ A_{res }≤ 2A.$