Long-wavelength source approximation ($d/\tau \ll 1$)

Dropping the position-dependent source delay in the leading far-zone retarded field requires source size $d$ to be small compared with its variation time $\tau$, in units $c=1$. The retarded quadrupole field also requires $d/r\ll 1$. For a typical nonrelativistic bound source, $\tau \sim d/v$ implies this long-wavelength condition; an arbitrarily rapidly oscillating small displacement is not controlled merely by its instantaneous speed.