Longitudinal waves in a dusty plasma are studied using fluid models wh
ere we regard the dust as being immobile. The variation of the charge
on the dust particles due to the wave field is taken into account. Thr
ee wave modes are considered; the ion-acoustic wave, the electrostatic
ion cyclotron (EIC) wave, and the Langmuir wave. We find that the dus
t charge variation and the wave field have a phase shift relative to e
ach other which influence the wave dispersion and normally lead to an
energy transfer between the waves and the plasma. The low frequency lo
ngitudinal waves such as the ion-acoustic wave and EIC wave are damped
, while the high frequency longitudinal Langmuir wave grows. The dampi
ng rate and the growth rate depend on the ratio between dust charge de
nsity and electron charge density, and are proportional to the dust ch
arging frequency OMEGA(C).