16. At the location of the detector, the phase difference between the wave which traveled straight down the tube and the other one which took the semi-circular detour is ∆φ = k∆d =
2π (πr − 2r) . λ
For r = rmin we have ∆φ = π, which is the smallest phase difference for a destructive interference to occur. Thus λ 40.0 cm rmin = = = 17.5 cm . 2(π − 2) 2(π − 2)