The half‐order derivative (d/dt)1/2s(t) is calculated fors(t) given by a burst of sine waves. The burst isNcycles in length, whereNis an integer or a half‐odd‐integer. The result contains Fresnel integrals; it may be written in a compact form by using the auxiliary Fresnel‐integral function usually denoted byg. Some novel properties ofgwere derived to facilitate a discussion of the result. The calculation is applicable to several dissipationless acoustical models for which the response to an exp(−iωt) input is proportional to ω1/2 exp(−iωt−iπ/4). Some examples include the pressure radiated by two‐dimensional sources such as the optoacoustic radiation from a thin modulated laser beam. Another example is the pressure from virtual ringlike sources such as those present in focused backscattering from large spheres and a torus. The scattering from a large torus is modeled for the case of an incident plane wave which propagates parallel to the symmetry axis.