Two identical circular wave sources, P and Q, oscillate on the surface of a large water tank with the same frequency f and amplitude a. The sources are separated by a distance d=5λ, where λ is the wavelength of the waves they generate. The sources are driven so that their oscillations start simultaneously but with a constant phase difference ϕ=3π.
(1) Part 1: (a) Along the line connecting P and Q, point R is located 2λ from P. Using qualitative reasoning and an appropriate geometric or vector representation, determine whether point R experiences constructive interference, destructive interference, or neither. Justify your choice.
(2) Part 2: (b) Develop a general expression for the resultant wave amplitude at R in terms of a, ϕ, and the path‐length difference Δℓ between waves arriving from P and Q. Clearly define all symbols used in your expression.
(3) Part 3: (c) For the specific values given, compute the ratio of the resultant amplitude at R to the individual source amplitude a. Show each step in your reasoning.
(4) Part 4: (d) The phase difference between the two sources is now slowly increased from ϕ=3π to ϕ=π. Describe qualitatively how the amplitude at R changes throughout this adjustment, and explain the physical basis for any non‐monotonic behavior.