The sonar equation rests on the assumption that received sound pressure level after scattering can be written in decibels as a sum of four terms: source level, transmission loss from the source to the target, target strength, and transmission loss from the target to the receiver. This assumption is generally not valid for scattering in a shallow water waveguide and can lead to large errors and inconsistencies in estimating a target's scattering properties as well as its limiting range of detection. By application of coherent waveguide scattering theory, the sonar equation is found to become approximately valid in a shallow water waveguide when the object's complex scatter function is roughly constant over the equivalent horizontal grazing angles +/- delta psi spanned by the dominant waveguide modes. This is approximately true (1) for all objects of spatial extent L and wavelength lambda when 2delta psi<lambda/2L and (2) for spheres and certain other rounded objects in nonforward scatter azimuths, even when (1) does not hold. The sonar equation may be made valid by lowering the active frequency of operation in a waveguide. This is often desirable because it greatly simplifies the analysis necessary for target classification and localization. Similarly, conditions are given for when Babinet's principle becomes approximately valid in a shallow water waveguide.