>/y i8, 1878] 



NATURE 



319 



THE EXPLANATION OF CERTAIN ACOUSTI- 

 CAL PHENOMENA ^ 



TV/I USICAL sounds have their origin in the vibrations of mate- 

 rial systems. In many cases, e.g. the pianoforte, the 

 vibrations are free, and are then necessarily of short duration. 

 In other cases, e.g. organ pipes and instniments of the violin 

 class, the vibrations are maintained, which can only happen 

 w hen the vibrating body is in connection with a source of energy 

 capable of compensating the loss caused by friction and genera- 

 tion of aerial waves. The theory of free vibrations is tolerably 

 complete, but the explanations hitherto given of maintained 

 vibrations are generally inadequate, and in most cases altogether 

 illusoiy. 



In consequence of its connection with a source of energy, a 

 vibrating body is subject to certain forces, whose nature and 

 effects are to be estimated. These forces are divisible into two 

 groups. The first group operate upon the periodic time of the 

 vibration, i.e. upon the pitch of the resulting note, and their 

 effect may be in either direction. The second group of forces 

 do not alter the pitch, but either encourage or discourage the 

 vibration. In the first case only can the vibration be maintained ; 

 so that for the explanation of any maintained vibration, it is 

 necessary to examine the character of the second group of forces 

 sxifficiently to discover whether their effect is favourable or un- 

 favourable. In illustration of these remarks, the simple case of 

 a common pendulum was considered. The effect of a small 

 periodic horizontal impulse is in general both to alter the periodic 

 time and the amplitude of vibration. If the impulse (supposed 

 to be always in the same direction) acts when the pendulum 

 passes through its lowest position, the force belongs to the second 

 group. It leaves the periodic time unaltered, and encourages or 

 discourages the vibration according as the direction of the pen- 

 dulum's motion is the same or the opposite of that of the impulse. 

 If, on the other hand, the impulse acts when the pendulum is at 

 one or other of the limits of its swing, the effect is solely on the 

 periodic time, and the vibration is neither encouraged nor dis- 

 couraged. In order to encourage, i.e. practically in order to 

 maintain a vibration, it is necessary that the forces should not 

 depend solely upon the position of the vibrating body. Thus, 

 in the case of the pendulum, if a small impulse in a given direc- 

 tion acts upon it every time that it passes through its lowest 

 position, the vibration is not maintained, the advantage gained 

 as the pendulum makes a passage in the same direction as that 

 in which the impulse acts being exactly neutralised on the return 

 passage, when the motion is in the opposite direction. 



As an example of the application of these principles, the 

 maintenance of an electric tuning-fork was discussed. If the 

 magnetic forces depended only upon the position of the fork, 

 the vibration could not be maintained. It appears, therefore, 

 that the explanations usually given do not touch the real point 

 at all. The fact that the vibrations are maintained is a proof 

 that the forces do not depend solely upon the position of the 

 fork. The causes of deviation are two : the self-induction of 

 the electric currents, and the adhesion of the mercury to the wire 

 whose motion makes and breaks the contact. On both accounts 

 the magnetic forces are more powerful in the latter than in the 

 earlier part of the contact, although the position of the fork is 

 the same ; and it is on this difference that the possibility of main- 

 tenance depends. Of course the arrangement must be such that 

 the retardation of force encourages the vibration, and the 

 arrangement which in fact encourages the vibration would have 

 had the opposite effect, if the niture of electric currents had 

 been such that they were more powerful during the earlier than 

 during the later stages of a contact. 



In order to brhag the subject within the limits of a lecture, one 

 class of maintained vibrations was selected for discussion, that, 

 namely, of which heat is the motive power. The best under- 

 stood example of this kind of maintenance is that afforded by 

 Trevelyan's bars, or rockers. A heated brass or copper bar, so 

 shaped as to rock readily from one point of support to another, 

 is laid upon a cold block of lead. The communication of heat 

 through the point of support expands the lead lying immediately 

 below in such a manner that the rocker receives a small impulse. 

 During the interruption of the contact the communicated heat 

 has time to disperse itself in some degree into the mass of lead, 

 and it is not difficult to see that the impulse is of a kind to 

 encourage the motion. But the most interesting vibrations of 



'■ Friday Evening Lecture, by Lord Rayleigh, M.A., F.R.S., March 15, 

 at the Royal Ics.itution of Great Britain. 



this class are thoje in which the vibrating body consists of a 

 mass of air more or less completely confined. 



If heat be periodically communicated to, and abstracted from, 

 a mass of air vibrating (for example) in a cylinder bounded by 

 a piston, the effect produced will depend upon the phase of the 

 vibration at which the transfer of heat takes place. If heat be 

 given to the air at the moment of greatest condensation, or taken 

 from it at the moment of greatest rarefaction, the vibration is 

 encouraged. On the other hand, if heat be given at the moment 

 of greatest rarefaction, or abstracted at the moment of greatest 

 condensation, the vibration is discoiu-aged. The latter effect 

 takes place of itself, when the rapidity of alternation is neither 

 very great nor very small, in consequence of radiation ; for when 

 air is condensed it becomes hotter, and communicates heat to 

 surrounding bodies. The two extreme cases are exceptional, 

 though for different reasons. In the first, which corresponds to 

 the suppositions of Laplace's theory of the propagation of sound, 

 there is not sufficient time for a sensible transfer to be effected. 

 In the second the temperatiu-e remains nearly constant, and the 

 loss of heat occurs during the process of condensation, and not 

 when the condensation is effected. This case corresponds to 

 Newton's theory of the velocity of sound. When the transfer of 

 heat takes place at the moments of greatest condensation or of 

 greatest rarefaction, the pitch is not affected. 



If the air be at its normal density at the moment when the 

 transfer of heat takes place, the vibration is neither encouraged 

 nor discouraged, but the pitch is altered. Thus the pitch is 

 raised, if heat be communicated a quarter period before the phase 

 of greatest condensation, and the pitch is lowered if the heat be 

 communicated a quarter period after the phase of greatest 

 condensation. 



In general both kinds of effects are produced by a periodic 

 transfer of heat. The pitch is altered, and the vibrations are 

 either encouraged or discouraged. But there is no effect of the 

 second kind if the air concerned be at a loop, i.e., a place where 

 the density does not vary, nor if the communication of heat be 

 the same at any stage of rarefaction, as in the corresponding 

 stage of condensation. 



The first example of aerial vibrations maintained by heat was 

 found in a phenomenon which has often been observed by glass- 

 blowers, and was made the subject of a systematic investigation 

 by Dr. Sondhauss. When a bulb about three quarters of an 

 inch in diameter is blown at the end of a somewhat narrow tube, 

 5 or 6 inches in length, a sound is sometimes heard proceeding 

 from the heated glass. It was proved by Sondhauss that a 

 vibration of the glass itself is no essential part of the pheno- 

 menon, and the same observer was very successful in discovering 

 the connection between the pitch of the note and the dimensions 

 of the apparatus. But no explanation (worthy of the name) of 

 the production of sound has been given. 



For the sake of simplicity, a simple tube, hot at the closed 

 end and getting gradually cooler towards the open end, was 

 first considered. At a quarter of a period before the phase of 

 greatest condensation (which occurs almost simultaneously at all 

 parts of the column) the air is moving inwards, i.e. towards the 

 closed end, and therefore is passing from colder to hotter 

 parts of the tube ; but the heat received at this moment (of 

 normal density) has no effect either in encouraging or dis- 

 couraging the vibration. The same would be true of the entire 

 operation of the heat, if the adjustment of temperature were 

 instantaneous, so that there was never any sensible difterence 

 between the temperatures of the air and of the neighbouring parts 

 of the tube. But in fact the adjustment of temperature takes time, 

 and thus the temperature of the air deviates from that of the 

 neighbouring parts of the tube, inclining towards the tempera- 

 ture of that part of the t\ib& from which the air has just come. 

 From this it follows that at the phase of greatest condensation 

 heat is received by the air, and at the phase of greatest rarefac- 

 tion is given up from it, and thus there is a tendency to maintain 

 the vibrations. It must not be forgotten, however, that apart 

 from transfer of heat altogether, the condensed air is hotter than 

 the rarefied air, and that in order that the whole effect of heat 

 may be on the side of encouragement, it is necessary that, pre- 

 vious to condensation, the air should pass not merely towards 

 a hotter part of the tube, but towards a part of the tube which 

 is hotter than the air will be when it arrives there. On this 

 account a great range of temperature is necessary for the main- 

 tenance of vibration, and even with a great range the influence 

 of the transfer of heat is necessarily unfavourable at the closed 

 end, where the motion is very small. Thi^ i^ probably the reason 



