Pocklington in 1879 proposed a simplified one-dimensional integral equation relating the current at the surface of a straight finite wire to the tangential trace of an incident electromagnetic field. This equation has been derived assuming that the current is constant across any section of the wire. At least for the model problem of a finite, straight and cylindrical wire, this simplified equation has been proved to be well posed. However, to our knowledge, there has been no rigorous study of the error between the solution of the exact integral equation and the solution of Pocklington's equation. We address this problem for the model case of acoustics in a smooth geometry.