AbstractThe plane transmission problem of the Helmholtz equation for quadrants is characterized by a one‐dimensional singular integral equation, which refers to the Fourier transform of the normal derivative of the solution along thex‐axis. It is derived by solving the transmission problem for the upper and the lower half‐plane involving a Neumann condition aty= 0. This is done by a two‐dimensional Laplace transform technique. The inverse Laplace transform with respect to the second cartesian coordinate and the restriction of this one toy= 0 then lead to the integral equation. Thereby the transmission conditions of the original problem aty= 0 have to be taken into account. The resulting integral equation is of generalized Wiener‐Hopf‐type. It is solved via the contraction theorem imposing restricting conditions on the w