The acoustic signal velocities for pressure modes in an infinite rectangular hard‐walled duct with a steady flow are investigated for the purpose of clarifying the degeneration of wave propagation which occurs with a low‐frequency sinusoidal excitation. It is found that all pressure modes propagate both upstream and downstream at a speed governed by the Doppler effect. All modes other than the plane wave are dispersive and leave a lingering disturbance after passage. In steady sinusoidal excitation, this lingering disturbance gives rise to cancellations and reinforcements which can cause nearly complete attenuation in the cutoff condition or can cause waves with negative phase velocities in the downstream section of the duct even without end reflections.