Longitudinal-acoustic (LA) phonons have been studied by inelastic x-ray scattering in the high-pressure incommensurate host-guest system Rb-IV in the pressure range of 16.3 to 18.4 GPa. Two LA-like phonon branches are observed along the direction of the incommensurate wave vector, which are attributed to separate lattice vibrations in the host and guest subsystems. The derived sound velocities for the host and the guest, v(h) and v(g), respectively, are similar in magnitude [v(h)=v(g)=3840(100) m/s at 18 GPa], but our results indicate rather different pressure dependences of dv(h)/dP=140(60) m/s GPa(-1) and dv(g)/dP=280(80) m/s GPa(-1). The observations for the one-dimensional Rb guest chains are reproduced quantitatively on the basis of the monatomic linear chain model and the measured compressibility of the chains.