  Small-scale locomotion plays an important role in biology. Different
modelling approaches have been proposed in the past. The simplest model is an
infinite inextensible two-dimensional waving sheet, {originally introduced by
Taylor}, which serves as an idealized geometrical model for both spermatozoa
locomotion and ciliary transport in Stokes flow. Here we complement classic
steady-state calculations by deriving the transient low-Reynolds number
swimming speed of such a waving sheet when starting from rest (small-amplitude
initial-value problem). We also determine the transient fluid flow in the
`pumping' setup where the sheet is not free to move but instead generates a net
fluid flow around it. The time scales for these two problems, which in general
govern transient effects in transport and locomotion at low Reynolds numbers,
are also derived using physical arguments.
