  We use inelastic neutron scattering to study spin waves and their correlation
with the magnetoelectric effect in Y$_{0.7}$Lu$_{0.3}$MnO$_3$. In the undoped
YMnO$_3$ and LuMnO$_3$, the Mn trimerization distortion has been suggested to
play a key role in determining the magnetic structure and the magnetoelectric
effect. In Y$_{0.7}$Lu$_{0.3}$MnO$_3$, we find a much smaller in-plane
(hexagonal $ab$-plane) single ion anisotropy gap that coincides with a weaker
in-plane dielectric anomaly at $T_N$. Since both the smaller in-plane
anisotropy gap and the weaker in-plane dielectric anomaly are coupled to a
weaker Mn trimerization distortion in Y$_{0.7}$Lu$_{0.3}$MnO$_3$ comparing to
YMnO$_3$ and LuMnO$_3$, we conclude that the Mn trimerization is responsible
for the magnetoelectric effect and multiferroic phenomenon in
Y$_{1-y}$Lu$_{y}$MnO$_{3}$.
