Abstract
Simple harmonic vibrations satisfying the equation are studied. In this equation, is the velocity potential, and denote Bessel and Legendre functions respectively, and and are polar coordinates. The parameter specifying the orders of the Bessel and Legendre functions is determined so that the vibrations satisfy the boundary conditions for a conical horn. This is possible by means of a new expansion for which is herein developed. With the assumption of a loop at the opening of the horn and by the aid of an asymptotic expansion for , numerical values are computed, for horns of various angles (2° to 30°) and for two types of vibration, of the ratios of several frequencies to the fundamental frequency , and of the ratios of the corresponding wave-lengths to the diameter of the horn at the opening. The nature of these two types of vibration is indicated by figures.
- Received 11 June 1924
DOI:https://doi.org/10.1103/PhysRev.25.218
©1925 American Physical Society