We demonstrate freely suspended graphene-based nanomechanical membranes (NMMs) as acoustic sensors in the audible frequency range. Simple and low-cost procedures are used to fabricate NMMs with various thicknesses based on graphene layers grown by graphite exfoliation and solution processed graphene oxide. In addition, NMMs are grafted with quantum dots (QDs) for characterizing mass sensitive vibrational properties. Thickness, roughness, deformation, deflection and emissions of NMMs with attached QDs are experimented and analyzed by utilizing atomic force microscopy, Raman spectroscopy, laser induced deflection analyzer and spectrophotometers. Förster resonance energy transfer (FRET) is experimentally achieved between the QDs attached on NMMs and nearby glass surfaces for illustrating acousto-optic utilization in future experimental implementations combining vibrational properties of NMMs with optical emission properties of QDs. This property denoted as vibrating FRET (VFRET) is previously introduced in theoretical studies while important experimental steps are for the first time achieved in this study for future VFRET implementations. The proposed modeling and experimental methodology are promising for future novel applications such as NMM based biosensing, photonics and VFRET based point-of-care (PoC) devices.