The scattering problem of an incident plane sound wave by a soft arbitrarily shaped body as well as its allied diffraction problem by a disk is discussed. A first‐class Fredholm integral equation is posed which, for low frequencies, yields a potential equations sequence for a wavenumber power solution expansion. The power solution expansion coefficients of the scattering cross section and the farfield amplitude up to O(κ6), where κ is the wavenumber, are found to be related through only a few low‐order solutions of the above equations. Reciprocity relations between them were exploited. The following new general formulas are obtained. The scattering cross‐section coefficient σ4 of O(κ4) is found in terms of three solutions up to O(κ2), rather than six solutions up to O(κ5). As for the farfield amplitude, the sixth (fifth, fourth, and third) coefficient of O(κ5) (κ4, κ3, and κ2) is related to only six (five, four, and two) solutions up to O(κ3) (κ2, κ, and κ). As an application of the above results, the coefficient σ4 is explicitly calculated using newly found solutions for an elliptic disk. Also, the circular disk results are shown for an arbitrary angle of incidence.