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We report the results of the investigation of bulk and surface acoustic phonons in the undoped and boron-doped single-crystal diamond films using the Brillouin-Mandelstam light scattering spectroscopy. The evolution of the optical phonons in the same set of samples was monitored with Raman spectroscopy. It was found that the frequency and the group velocity of acoustic phonons decrease nonmonotonically with the increasing boron doping concentration, revealing pronounced phonon softening. The change in the velocity of the shear-horizontal and the high-frequency pseudo-longitudinal acoustic phonons in the degenerately doped diamond, as compared to that in the undoped diamond, was as large as ∼15% and ∼12%, respectively. As a result of boron doping, the velocity of the bulk longitudinal and transverse acoustic phonons decreased correspondingly. The frequency of the optical phonons was unaffected at low boron concentration but experienced a strong decrease at the high doping level. The density-functional-theory calculations of the phonon band structure for the pristine and highly doped samples confirm the phonon softening as a result of boron doping in diamond. The obtained results have important implications for thermal transport in heavily doped diamond, which is a promising material for ultra-wide-band-gap electronics.