We study the spin dynamics of the manganites ${\mathrm{La}}_{0.9}{\mathrm{Ca}}_{0.1}\mathrm{Mn}{\mathrm{O}}_{3}$ and ${\mathrm{La}}_{0.91}{\mathrm{Sr}}_{0.09}\mathrm{Mn}{\mathrm{O}}_{3}$ in magnetic field. Previous studies in zero field have shown that the magnetic ground state is inhomogeneous with ferromagnetic $(F)$ droplets embedded in a canted antiferromagnetic (CAF) matrix. The spin dynamics consists of two spin wave branches in a high and a low-energy range, respectively. However, the assignment of these two branches either to a mean CAF medium or to $F$ droplets embedded in an AF matrix, was uncertain. The present study shows that these two branches do not follow the mean-field calculation for a homogeneous CAF state and do not correspond either to a phase separation between AF and $F$ states. The progressive spin-flop transitions observed for $H\ensuremath{\Vert}\mathbf{b}$ and $H\ensuremath{\Vert}\mathbf{a}+\mathbf{b}$, give rise to strong changes in the dispersion of the spin waves. The low-energy branch, only visible around $F$ zone centers at zero field, appears at any $q$-value in magnetic field. Moreover, as soon as the AF spin component deviates from its easy axis, leading to a decrease of the magnetic anisotropy, the high-energy branch is no more defined near the zone boundary. Its intensity is transferred to a higher flat level, likely related to defects in the CAF matrix. These new results strongly support a picture where these magnetic excitations arise from a modulated canted antiferromagnetic ground state consisting of two coupled $F$ and AF components.