Sound field reproduction algorithms require loudspeaker directivity, which is usually measured at discrete frequencies. A time domain model of loudspeaker directivity benefits broadband applications. This Letter proposes the concept of a directional wave front in the time domain, which could be linked to loudspeaker impulse responses measured on a spherical surface. The observed signal in the time domain at the boundary of a spherical region due to a propagating directional wave front is illustrated using a geometric model. Based on the geometric model, the spherical harmonic decomposition of the observed signal in the time domain is also derived.