We consider the propagation of hydromagnetic waves generated by a compact turbulent source in low ionized plasmas, applying the Lighthill theory. We assume the plasma to be isothermal, and adopt a uniform, stationary medium thread by ordered magnetic fields as an initial condition. Then, the distinct properties of the hydromagnetic waves originating from a source oscillating with a fixed frequency are studied in the linear regime. As is well known, in low ionized plasmas, the generated waves dissipate due to ion-neutral damping. In this paper, the dependence of the dissipation rate on the frequency of the oscillating source is investigated. The larger the frequency becomes, the more substantial is the wave dissipation. Implications of our results on the energy source in molecular clouds are also discussed. Interestingly, since the outflow lobes associated with young stellar objects act as compact turbulent sources, hydromagnetic waves are generated by them. From our order-estimations, about 70% of the energy of the outflow itself propagates as waves or turbulences, while the remaining 30% dissipates and heats the neutrals via ion-neutral damping. Then, we confirm that the outflows are significant energy sources in molecular clouds in the context of the Lighthill theory.