Wave propagation and attenuation in a classical flow metering device, the Herschel–Venturi tube, is investigated analytically and experimentally. The analytical results are shown to compare well with the experimental observations for anechoically terminated Herschel–Venturi tubes. In the absence of flow, the Taylor series approximations to the governing differential equations and the stepwise expansion and contraction method are shown to be identical. The effect of mean flow on the wave attenuation performance of Herschel–Venturi tubes is also studied in terms of a solution obtained by the Runge–Kutta method, and the applicability of the stepwise expansion and contraction method is discussed with the mean flow through the duct.