The transient behavior of a small-signal, plane, progressive sound wave in a viscous fluid is considered. In terms of the particle velocity u, the boundary condition is u(0,t)=u0H(t) sin ωt, where H(t) is the unit step function. By making an approximation, we transform the viscous wave equation into the heat equation and thereby obtain the solution u/u0=e−αx siny+12e−y2/AαxIm[w(A+jy/2A)], where y−ωt−kx, A=(αx)12, α is the viscous attenuation coefficient, and w(z) is the error function of complex argument [Natl. Bur. Std. Handbook of Mathematical Functions, AMS 55, p. 297 (1964)]. The first term is the steady-state solution. The second term “annihilates” the steady-state solution in the region x>ct (i.e.. ahead of the wavefront) and also contains the transient solution. The latter is important in the neighborhood of the wavefront and in particular gives the wave a precursor. The possibility of observing this precursor experimentally is discussed. [Work supported by the U. S. Air Force Office of Scientific Research, Office of Aerospace Research.]