It is shown that this problem can be reduced to the same mathematical form as the equivalent smooth‐walled problem. Consequently, the form of the general expressions obtained for the distribution of scattered acoustic intensity among the waveguide modes and for the azimuthal beam pattern in a specified waveguide mode obtained in an earlier paper [G. R. Sutton and J. J. McCoy, J. Acoust. Soc. Am. 60, 833–839 (1976)] are appropriate to this more general problem.