Objective To solve the problems of the fluctuating pressure and acoustic radiation of a cascade in turbulence, the theory of the cascade response function is introduced and analyzed.

Methods The theory assumes that cascade blades have no thickness, and the integral expression of the cascade scattering field is solved by the Wiener−Hopf method, so that the analytical expression of the velocity potential of the cascade scattering field and the unsteady pressure coefficient of the cascade surface can be obtained, and the radiated sound power of the outer watershed of the cascade can be further obtained. The pressure coefficient and radiated sound power of the cascade are calculated by the analytical formula and compared with the results of the numerical method. The function is further extended to underwater, and the unsteady forces predicted by the cascade response function and Sears function are compared.

Results The results obtained by the analytical method and numerical method are consistent.The frequency spectrum curves of the cascade unsteady lift coefficient calculated by the cascade response function and Sears function have the same trend.

Conclusion The calculated results of the cascade response function are slightly lower than those of the Sears function in amplitude. However, compared with the cascade response function, the Sears function in a single wavenumber domain cannot take into account the effects of the placement angle, trim and sideslope on the unsteady lift of the cascade.