  We investigate the propagation and evolution for a massless scalar field in
the background of $\lambda=1/2$ Ho\v{r}ava-Lifshitz black hole with the
condition of detailed balance. We fortunately obtain an exact solution for the
Klein-Gordon equation. Then, we find an analytical expression for the greybody
factor which is valid for any frequency; and also exactly show that the
perturbation decays without any oscillation. All of these can help us to
understand more about the Ho\v{r}ava-Lifshitz gravity.
