  High-resolution ($\Delta E$=1.3 meV) inelastic X-ray scattering (IXS) in
optimally doped untwinned YBa$_2$Cu$_3$O$_{7-\delta}$ single crystals show that
the dispersion of transverse acoustic phonons in the a-direction remains linear
with no softening due to bending modes in the long wavelength limit, down to
q=0.02. The sound velocity is found to be 2700 +/- 70 m s$^{-1}$, in excellent
agreement with ultrasound measurements, and unchanged upon cooling from room
temperature to 98 K. These results rule out a strong coupling between bending
dynamics of the CuO$_2$ planes and charge carriers in cuprates.
