The time dependent P1 approximation to the neutron transport equation has been solved for the case of an oscillating source on one face of a finite parallelepiped. An oscillatory solution to the differential equations describes the propagation of neutron waves through the medium. Attenuation lengths of plane neutron waves were identical at low frequencies (ω < ½ νΣa) for the P1 and diffusion approximations but differ considerably at high frequencies (ω > 2ν Σtr). Wave lengths and wave speeds for the two approximations were slightly different at low frequencies, identical at immediate frequencies and considerably different at high frequencies. A new method, which considers the transient behavior of a spatially-integrated positive-definite function of flux and current, is used to show that the transient part of the solution decays to zero.