  We consider an Ising spin-chain in a random transverse magnetic field and
compute the zero temperature wave vector and frequency dependent dynamic
structure factor numerically by using Jordan-Wigner transformation. Two types
of distributions of magnetic fields are introduced. For a rectangular
distribution, a dispersing branch is observed, and disorder tends to broaden
the dispersion peak and close the excitation gap. For a binary distribution, a
non-dispersing branch at almost zero energy is recovered. We discuss the
relationship of our work to the neutron scattering measurement in
$\mathrm{LiHoF_4}$.
