Abstract: The gradient of Sound field on the surface of any tube in the tube bundles has be expressed in term of the impedance condations of the pressure modes on the surface .The multiple scattering problem has be examined by applying the method of expansion of characteristic functions of a set, and arrived at a set of linear algebraic equations for the unknown coefficients of each tube. The numerical resullts in a tubes row consisting of five indentical tubes coincide well with the literature 3, for an array by consisting tubes it is proved that for oblique wave incidence the sonic soot cleaning efficiency is best.