Capacitively coupled radio-frequency discharges have great significance for indus- trial applications. Collisionless electron heating in such discharges is important, and sometimes is the dominant mechanism. This heating is usually understood to orig- inate in a stochastic interaction between electrons and the electric fields. However, other mechanisms may also be important. There is evidence of wave emission with a frequency near the electron plasma frequency, i.e. ωpe , from the sheath region in collisionless capacitive radio-frequency (RF) discharges. This is the result of a progressive breakdown of quasi-neutrality close to the electron sheath edge. These waves are damped in a few centimeters during their propagation from the sheath towards the bulk plasma. The damping occurs because of the Landau damping or some related mechanism. This research work reports that the emission of waves is associated with a field reversal during the expanding phase of the sheath. Trapping of electrons near to this field reversal region is observed. The amplitude of the wave increases with increasing RF current density amplitude J˜0 until some maximum is reached, beyond which the wave diminishes and a new regime appears. In this new regime, the density of the bulk plasma suddenly increases because of ion reflection which occurs due to presence of strong field reversal near sheath region. Our calcu- lation shows that these waves are electron plasma waves. These phenomena occur under extreme conditions (i.e. higher J˜0 than in typical experiments) for sinusoidal current waveforms, but similar effects may occur with non-sinusoidal pulsed wave- forms for conditions of experimental interest, because the rate of change of current is a relevant parameter. The effect of electron elastic collisions on plasma waves is also investigated.