The “gravitational memory effect” due to an exact plane wave provides us with an elementary description of the diffeomorphisms associated with the analogue of “soft gravitons for this nonasymptotically flat system. We explain how the presence of the latter may be detected by observing the motion of freely falling particles or other forms of gravitational wave detection. Numerical calculations confirm the relevance of the first, second and third time integrals of the Riemann tensor pointed out earlier. Solutions for various profiles are constructed. It is also shown how to extend our treatment to Einstein-Maxwell plane waves and a midisuperspace quantization is given.