  We are interested in the phonon response in the frustrated magnets
SrCr$_{9x}$Ga$_{12-9x}$O$_{19}$ (SCGO) and
Ba$_{2}$Sn$_{2}$ZnCr$_{7x}$Ga$_{10-7x}$O$_{22}$ (BSZCGO). The motivation of the
study is the recently discovered, phonon-driven, magnetic relaxation in the
SCGO compound [Mutka et al. PRL {\bf 97} 047203 (2006)] pointing out the
importance of a low-energy ($\hbar\omega\sim$7 meV) phonon mode. In neutron
scattering experiments on these compounds the phonon signal is partly masked by
the magnetic signal from the Cr moments and we have therefore examined in
detail the non-magnetic isostructural counterparts SrGa$_{12}$O$_{19}$ (SGO)
and Ba$_{2}$Sn$_{2}$ZnGa$_{10}$O$_{22}$ (BSZGO). Our {\it ab-initio} lattice
dynamics calculations on SGO reveal a peak in the vibrational density of states
matching with the neutron observations on SGO and SCGO. A strong contribution
in the vibrational density of states comes from the partial contribution of the
Ga atoms on the 2b and 12k sites, involving modes at the M--point of the
hexagonal system. These modes comprise dynamics of the kagom\'e planes of the
pyrochlore slab magnetic sub-lattice, 12k sites, and therefore can drive
magnetic relaxation via spin-phonon coupling. Both BSZCGO and BSZGO show a
similar low-energy Raman peak but no corresponding peak in the neutron
determined density of states of BSZGO is seen. However, a strong non-Debye
enhancement of low-energy phonon response is observed. We attribute this
particular feature to the Zn/Ga disorder on the 2$d$ -site, already evoked
earlier to affect the magnetic properties of BSZCGO. We propose that this
disorder-induced phonon response explains the absence of a characteristic
energy scale and the much faster magnetic relaxation observed in BSZCGO.
