This work considers the propagation of sound in a waveguide with an impedance wall. In the low frequency regime, the first effect of the impedance is to decrease the propagation speed of acoustic waves. Therefore, a flow in the duct can exceed the wave propagation speed at low Mach numbers, making it effectively supersonic. This work analyzes a setup where the impedance along the wall varies such that the duct is supersonic then subsonic in a finite region and supersonic again. In this specific configuration, the subsonic region acts as a resonant cavity, and triggers a laser-like instability. This work shows that the instability is highly subwavelength. Besides, if the subsonic region is small enough, the instability is static. This work also analyzes the effect of a shear flow layer near the impedance wall. Although its presence significantly alters the instability, its main properties are maintained. This work points out the analogy between the present instability and a similar one in fluid analogues of black holes known as the black hole laser.
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