The equations appropriate to the propagation of sound in a realistic jet flow have been solved by finite‐difference methods for the case of a sinusoidal point source on the axis of a subsonic jet. Each numerical solution provides detailed phase and amplitude information throughout the sound field. At the high‐frequency limit the finite‐difference results agree with ray‐tracing results. Also, the computed farfield directivity patterns generally agree with available experimental data and lend further support to the view that the downstream “valley” in jet noise is due to refraction rather than to the inherent directivity of the sound generated within the region of turbulence. Unexpected findings are that the flow beyond 100 nozzle diameters continues to deepen the refraction valley significantly, and that the sound‐pressure level reduction at a fixed point on the axis at first increases as the source is moved downstream from the nozzle. For the application of the refraction results to the computation of jet noise directivity, is found that the distortion of the constant phase surfaces can be neglected except at high frequencies.