Q4. Two equal waves combine to give a resultant of amplitude √3 times the amplitude of either. What is their phase difference?
2a cos(φ/2) = √3 a gives cos(φ/2) = √3/2, so φ/2 = π/6 and φ = π/3.
Q5. Two sources in phase send equal waves to a point. The path difference is half a wavelength. What is the phase difference, and what happens there?
φ = 2π × (½) = π, so the waves arrive completely out of phase and interfere destructively: the resultant amplitude is zero.
Q6. At one instant two overlapping waves give displacements of +3 mm and −5 mm at a point. What is the displacement there?
By superposition, y = 3 + (−5) = −2 mm.