Consider a two-dimensional waveguide consisting of a rigid wall and a parallel wall having uniform specific impedance. When the impedance is purely imaginary, the characteristic equation is real. In the springlike case, the eigenvalue of the fundamental mode (defined as the mode that varies most slowly in the transverse direction) is imaginary, whereas all other eigenvalues are real. This type of mode does not exist if the impedance is masslike. Morse and Ingard [Theoretical Acoustics (McGraw-Hill, New York, 1968), p. 496] fail to recognize the differing behavior of the fundamental mode for either type of lossless impedance, and subsequently no one seems to have rectified this oversight. The fundamental mode in the springlike case behaves much like the plane mode in a hard-walled waveguide in that it has no cutoff frequency, but the phase speed of this mode is subsonic at all frequencies. Introducing a resistive part to the impedance, corresponding to dissipation at the wall, moves the respective eigenvalues off the real or imaginary axis. The presentation will discuss the phase and group speeds, and the transverse mode shapes, in ideal and lossy cases.