A clarifying analytical study was done for the 2-DOF acousto-mechanical system modeled as the Helmholtz resonator with elastic vibrating bottom. Generally, such a system has two resonances that can generate and radiate an annoying tonal noise. As shown, the two resonance frequencies may get very close with mutual amplification and even merge together into one powerful resonance (a close-form equation describing this transition was derived). Such an effect can happen because the mass of air in the neck and the rigid mass may differ in several orders of magnitude. This is less possible in 2-DOF mechanical systems where the masses of both vibrating rigid bodies are commonly within one order of magnitude. The results may be helpful in particular for noise identification and reduction in blowers and other air moving devices. Here, the role of a vibrating bottom is played by the impeller in combination with the rotor and suspension system, and the air inlet (or outlet) serves as the Helmholtz resonator neck. Low-frequency acousto-mechanical resonances can also occur in rooms with open windows or doors.