An Accurate Measurement of Displacement by Means of Sound Frequency in a Resonant Pipe : Theoretical Analysis of Sound Frequency Variation with Displacement of Substance

Abstract

A new accurate measurement of displacement by means of sound frequency variation in a resonant pipe has been investigated. This paper deals with the theoretical analysis of the sound frequency variation generated in the pipe. The acoustic input impedance and the acoustic radiation impedance between the pipe and a substance vary with the displacement of the substance which is placed at the other end of the pipe. Those two impedances are introduced as part of the new concept and the sound frequency variation is calculated with these impedances. The results of sample calculations and experiments coincide significantly.