Part I.―The experimental analysis of a sound in air and water: Some experiments towards a sound spectrum. - Part II.―The theory of analysis of an electric current by periodic interruption

Abstract

A method of analysing an alternating current termed “Analysis by Periodic Interruption” was worked out by G. Barlow in May, 1916, and is described by him in some detail in Part II. The present paper, Part I., gives an account of certain experiments in which this method has been applied to the analysis of sound vibrations in air and water with the object of obtaining “ sound spectra.” The principle of the method may be stated as follows. The alternating current circuit contains a direct current galvanometer and also an interrupter of which the speed can be varied over the whole range of frequency to be investigated. Generally the type of interrupter used is such that the intervals during which the circuit is open and closed are equal. When the interruptions synchronize with any component A sin 2 πnt of the current, fig. 1 ( a ), the galvanometer responds by giving a steady deflection of magnitude depending on the phase difference. Fig. 1 ( b ) shows interruptions and current in the same phase. Practically it is better to allow a slight difference in frequency; the galvanometer then oscillates slowly to and fro as the phase alters. The maximum amplitude of the galvanometer swings is then proportional to the amplitude A of the component current—actually it measures A In.In making the analysis the frequency of interruption is slowly increased over the whole range. The approach to the condition of synchronism is indicated by a rapid oscillation of small amplitude followed by slower oscillations of greater amplitude until the maximum is reached. Afterwards the oscillations die down in the reverse order. This characteristic motion exhibited by the galvanometer will be referred to by the term “response.” In this way the amplitude of each component may be determined. At the same time the corresponding frequency is obtained by observing, at the moment of maximum, the frequency at which the interrupter is driven. For a component of given amplitude the range of frequency over which the response is greater than half its maximum value, and which may be called the “width of response,” is the same at all frequencies. For example, if a response at 10/sec. falls to half value for frequencies of interruption of 9 and 11/sec., then one at 1000/sec. will fall to half value at 999 and 1001/sec. It will therefore be seen that it is necessary to have perfect control over the speed of interruption, especially in the higher frequency region, and the same time must be spent in sweeping over a range such as 1000-1100/sec. as over 10-110/sec. In measuring a response the rate at which the speed of interruption may be changed is conditioned by the period of the galvanometer. It is necessary that the speed should not change sensibly during an interval of time of the order of the galvanometer period. The galvanometer may be of any type, but its vibrations should be well damped so as to be nearly dead-beat. A suitable period is 3 seconds. Under these conditions the width of response is 0.7/sec.