We consider a particular model of a `Source’ of independent particles and a macroscopic `Detector’ that are both tuned to the same resonance frequency ν0≡1/P. Particles are emitted by the Source at exact multiples of the resonance period P, and the Detector absorbs them with a certain probability at any one of its points. The Detector may also `announce’ the detection of the absorbed particle. Any particle that is not absorbed at a certain point passes through to a deeper layer in the interior of the Detector. Eventually, all particles will be absorbed (i.e. detected). We calculate the probability of detection of two time-series of particles generated by the same Source that reach the Detector with a time delay δt between themselves, and show that it manifests the illusion of collective (wave-like) interference with particle number conservation.