  The hidden ordered state of the frustrated pyrochlore oxide
Tb$_{2+x}$Ti$_{2-x}$O$_{7+y}$ is possibly one of the two electric multipolar,
or quadrupolar, states of the effective pseudospin-1/2 Hamiltonian derived from
crystal-field ground state doublets of non-Kramers Tb$^{3+}$ ions. These
long-range orders are antiparallel or parallel alignments of transverse
pseudospin components representing electric quadrupole moments, which cannot be
observed as magnetic Bragg reflections by neutron scattering. However
pseudospin waves of these states are composite waves of the magnetic-dipole and
electric-quadrupole moments, and can be partly observed by inelastic magnetic
neutron scattering. We calculate these spin-quadrupole waves using linear
spin-wave theory and discuss previously observed low-energy magnetic excitation
spectra of a polycrystalline sample with $x = 0.005$ ($T_{\text{c}} = 0.5 $ K).
