We investigated transverse acoustic (TA) phonons in iron-bearing magnesium oxide (ferropericlase) up to 56 GPa using inelastic x-ray scattering (IXS). The results show that the energy of the TA phonon far from the Brillouin zone center suddenly increases with increasing pressure above the spin transition pressure of ferropericlase. Ab initio calculations revealed that the TA phonon energy far from the Brillouin zone center is higher in the low-spin state than in the high spin state; that the TA phonon energy depend weakly on pressure; and that the energy gap between the TA and the lowest-energy-optic phonons is much narrower in the low-spin state than in the high-spin state. This allows us to conclude that the anomalous behavior of the TA mode in the present experiments is the result of gap narrowing due to the spin transition and explains contradictory results in previous experimental studies.