An optically excited Rydberg wavepacket can be generated by exciting the electron from a low-lying state to a coherent superposition of high-lying states with a short broadband optical pulse. A special kind of Rydberg wavepacket is generated in the case of a interaction of a weak THz half cycle pulse with a stationary Rydberg state, called the THz wavepacket. This THz wavepacket is a coherent superposition of the initial Rydberg state and its neighbouring states. We have investigated the time evolution of THz wavepackets by measuring the impact of two in time delayed half cycle pulses (»200 V cm-1) on the population of a stationary (n = 40) Rydberg state in rubidium. The first half cycle pulse creates the THz wavepacket and the second half cycle pulse probes the dynamics of the THz wavepacket. We support our experimental data by numerically solving the Schrödinger equation and with a semi-classical picture. Whereas an optically excited wavepacket is initially localized, a THz wavepacket is initially delocalized and becomes localized after half a revival time.