An atomistic effective Hamiltonian scheme is employed within Molecular Dynamics simulations to investigate how the electrical polarization and magnetization of the multiferroic BiFeO3 respond to time-dependent ac magnetic fields of various frequencies, as well as to reveal the frequency dependency of the dynamical (quadratic) magnetoelectric coefficient. We found the occurrence of vibrations having phonon frequencies in both the time-dependency of the electrical polarization and magnetization (for any applied ac frequency), therefore making such vibrations of electromagnonic nature, when the homogeneous strain of the system is frozen (case 1). Moreover, the quadratic magnetoelectric coupling constant is monotonous and almost dispersionless in the subTHz range in this case 1. In contrast, when the homogeneous strain can fully relax (case 2), two additional low-frequency and strain-mediated oscillations emerge in the time-dependent behavior of the polarization and magnetization, which result in resonances in the quadratic magnetoelectric coefficient. Such additional oscillations consist of a mixing between acoustic phonons, optical phonons and magnons, and reflect the existence of a new quasiparticle that can be coined “electroacoustic-magnon”. This latter finding can prompt experimentalists to shape their samples to take advantage of, and tune, the magnetostrictive-induced mechanical resonance frequency, in order to achieve large dynamical magnetoelectric couplings