Calculation of the energy scattered out of an advancing wave front allows one to derive an attenuation coefficient δ for the low‐frequency boundary mode carried by a rough interface between two media. For a point source of sound on or near the interface this leads to a farfield boundary wave pressurepB∝r−1/2f3/2e−δrwith δ=Af6, whereris the range,fis the frequency, andAis a parameter which depends upon the form and size of roughness (for close packing it is proportional to the fifth power of the roughness height). For givenr, then,pBmust exhibit a maximum in the frequency domain atf=(4Ar)−1/6and falls off sharply for higher frequencies. This paper gives a simple procedure for calculatingAfor bossy roughness models of two fluid interfaces. In the particular case of a hard rough boundary the theory predicts results in reasonable agreement with reported experimental results, at least insofar as the magnitude and shape of thepB(f) curve is concerned.