The explanation of the acoustical action of multiple Helmholtz resonators, except for one and two cavities, has not been developed. Application of Lagrange's method is made to obtain the equations of motion of the fluid displacements. The equation for the frequencies of resonance is obtained by placing the determinant of the coefficients of the displacements equal to zero. The calculations yield a number of resonances equal to the number of cavities in the system. These are found to be in agreement with the experimental results. This physical method of approach, rather than synthetic electrical circuit theory, affords, among other applications, a more direct and more informative method for explaining the resonances of the vocal tract.