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"Pumping" of phonons by a dynamic magnetization promises to extend the range and functionality of magnonic devices. We explore the impact of phonon pumping on room-temperature ferromagnetic resonance (FMR) spectra of bilayers of thin yttrium iron garnet (YIG) films on thick gadolinium gallium garnet substrates over a wide frequency range. At low frequencies the Kittel mode hybridizes coherently with standing ultrasound waves of a bulk acoustic resonator to form magnon polarons that induce rapid oscillations of the magnetic susceptibility, as reported before. At higher frequencies, the phonon resonances overlap, merging into a conventional FMR line, but with an increased line width. The frequency dependence of the increased line broadening follows the predictions from phonon pumping theory in the thick substrate limit. In addition, we find substantial magnon-phonon coupling of a perpendicular standing spin wave (PSSW) mode. This evidences the importance of the mode overlap between the acoustic and magnetic modes, and provides a route towards engineering the magnetoelastic mode coupling.