Finite amplitude sound near cutoff in higher‐order modes of a rectangular duct

The finite amplitude distortion of sound that is transmitted in a higher‐order mode of a rectangular duct is investigated both theoretically and experimentally. A perturbation solution is used to determine the general form of the governing equations for source frequencies near cutoff, where dispersive wave interactions may frequently be ignored. A set of coupled first‐order equations in terms of the harmonic amplitudes is obtained for the nondispersive interactions. Tube wall attenuation is included ad hoc. Experimental results are reported for the distortion of a 140‐dB (re: 20 μPa) tone transmitted in the (1,0) mode of an air‐filled rectangular duct. The cutoff frequency is 2470 Hz, and the theory for nondispersive interactions is in reasonable agreement with experimental results for source frequencies between approximately 2600 and 3300 Hz. Above 3300 Hz, the nonlinear interactions are strongly affected by dispersion. Below 2600 Hz, where thermoviscous absorption is very high, the predicted tube wall a...