The behaviour, in a moderator, of the neutron density wave propagating from a modulated thermal neutron source is studied. The Boltzmann equation, in the diffusion approximation, is solved numerically to obtain a complete set of complex eigenfunctions whose amplitudes are obtained from the oscillating source condition. By introducing an effective (complex) wave parameter the detector response as a function of time, and position is examined. The feasibility of measuring asymptotic values of the wave parameters, particularly when critical values of frequency and buckling have been exceeded, is investigated, and the effect of various source energy distributions demonstrated. The calculated values of the fundamental wave parameters α0, ξ0 are compared directly with the measured values of Perez and Booth, for a graphite system with B⊥2 = 000596 cm−2.