SCIENCE. 



613 



CORRESPONDENCE. 



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LOUDNESS vs. INTENSITY OF SOUND. 

 To the Editor of " SCIENCE." 



Will it seem like firing a blank cartridge at Copenha- 

 gen to urge that writers on acoustics ought more carefully 

 to distinguish between the words loudness and intensity 

 as applied to sound ? We think not, so long as state- 

 ments like the following are found in elemental-} - manu- 

 als of physics ; or so long as the language of even distin- 

 guished lecturers on Sound is not wholly free from similar 

 indefinite expressions. 



For instance, the law of variation in intensity of a 

 sound free to move in a homogeneous medium is often 

 stated in substance thus : the intensity or loudness of 

 sound decreases as the square of the distance. As an 

 illustration it is sometimes added, a sound at the distance 

 two will be only one fourth as loud as at the distance one. 

 While as a triumphant proof or verification of this law, 

 it is often said : a single bell at the distance of ten yards 

 will sound as loud as four similar bells at twenty yards. 



It is well known that the word sound and several of 

 the terms used in describing sound have two meanings. 

 The word loudness primarily refers to the sensation of 

 hearing. In order to avoid confusion of thought, I es- 

 teem it important that the use of this word be restricted 

 to the sensation, and that the word intensity ( or volume ) 

 shall refer solely to the external vibrations which are the 

 cause of the sensation. In other words, loudness ought 

 always to be used in a subjective, intensity in an objective, 

 sense. 



What is meant by such expressions as those above 

 quoted? Perhaps they are simply examples of a loose 

 use ot language, but it will certainly be natural fcr the 

 unwary reader to infer from them that loudness and in- 

 tensity vary according to the same laws, and also that we 

 can by the ear verify those laws. I have no hesitation in 

 affirming that this use either purposely or otherwise, of the 

 word loudness as synonymous with the word intensity, 

 has been the cause of great confusion of thought, and 

 has often loaded down the undulatory theory of sound 

 with that which is really foreign to it. The time has 

 come ■'vhen we ought to regard that treatise on sound as 

 a failure in one important respect which does not leave the 

 reader thoroughly imbued with the idea that the law of 

 variation in the intensity of a sound refers to sound vibra- 

 tions and not to the intensity of the sensation of hearing. 



But if those who use such expressions as have been 

 quoted, really mean to claim that loudness, i. e., relative 

 intensity of sensation, varies according to the same laws 

 as the energy of the moving molecules of the sound wave, 

 or if it is claimed that by the ear we can accurately and 

 validly verify the law, then it will be in order to demand 

 the proof. 



In order that such physiological laws may be proved 

 true it must be shown, either, i, that we can accurately 

 know when one of our sensations is a multiple of another 

 (as when one sound is four times as loud to the ear as 

 another), or, 2, that we can recognize sensations of equal 

 intensity ; and, 3, it must also be proved that the inten- 

 sity of the sensation is proportional to the energy of the 

 blow causing the sensation. These assumptions cannot 

 be proved. 



I. It goes without saying that any one having normal 

 senses can tell a heavy blow from a light one, and can re- 

 cognize degrees of intensity among sounds, lights, heats, 

 tastes, and smells. But if it is claimed that there are quan- 

 titative relations between sensations of different intensity, 

 and that we can by consciousness recognize these ratios, 

 we at once become committed to a remarkable system of 

 mathematics. Since experience shows that the senses 



are easily deceived and that different persons disagree as 

 to their estimates, who shall decide what are the true ra- 

 tios ? But we can only compare the relative intensities 

 of two sensations by memory. Here is a fruitful source 

 of uncertainty, for before we can be sure that one sound 

 is to our ears four times as loud as another, we must be 

 certain that we can by memory reproduce the first sensa- 

 tion and place it beside the second in exactly its true in- 

 tensity. No one can be sure of this. This reasoning 

 applies to those who have perfect senses, if there are such. 

 When we consider the myriad degrees of nerve sensi- 

 tiveness, partly congenital, partly the result of habit, and 

 partly the result ot disease, the problem becomes still 

 more difficult, ludicrously so. 



2. Can we recognize sensations of equal intensity? 

 No doubt we can do so much more exactly than we can 

 estimate the relation between sensations varying greatly 

 in intensity. Yet here we meet the same cause of doubt 

 as before, — the uncertainty of memory. The less is the 

 time intervening between two distinct and independent 

 sensations, the more nearly we can estimate their true in- 

 tensities. In compaiing sounds, somewhat more than 

 one sixteenth ot a second must elapse between them. 

 In the photometer the lights or shadows are shown in con- 

 trast and are thrown side by side upon the screen, where 

 we can see them simultaneously or pass from one to the 

 other very quickly. Probably there is no way whereby we 

 can compare two sensations more accurately than by the 

 photometer, yet no one will claim that he can move the 

 lights so that their intensities shall be exactly equal on 

 the screen. All he can say is : to the eye they are equal. 

 If then under the most favorable conditions, there is a 

 residuum of doubt, the sense of hearing will be still more 

 ■ untrustworthy ; I regard it, therefore, as a fallacious me- 

 thod of research to bring physical laws to be tested by the 

 uncertainties of sensation. Can feeling demonstrate the 

 accuracy of a thermometer, or can the laws of energy be 

 verified by striking ourselves blows with moving bodies ? 

 All that we can say is that within certain limits the testi- 

 mony of our senses approximately conforms to the laws 

 which have been deduced from more accurate observa- 

 tions and reasoning. 



3. Are sensations proportional to the energy of the 

 impacts producing them ? They must be, if loudness and 

 intensity vary according to the same laws, or if equal sen- 

 sations are caused by equal blows. The hypothesis is 

 manifestly absurd as a general law, for we are uncon- 

 scious of very weak blows, and very violent ones either 

 destroy the nerves or paralyze them by what is known as 

 shock. Even within the most favorable limits the rule can 

 ODly be approximately true, aDd if it were true, could not be 

 proved, for the nerves retain their impressions for a vari- 

 able length of time, and this marks a limit to the intervals 

 at which we can repeat impressions of norma) intensity 

 free from the residual effect of previous impressions. 

 Hence if impressions be repeated too soon they will gen- 

 erally cause a progressive deadening of the nerve sensi- 

 tiveness, or sometimes an increased sensitiveness, as in 

 the case of the punishment of the bastinado. Even if 

 there were nervous conditions such that the sensation was 

 proportional to the energy of the impact, it would be dif- 

 ficult if not impossible to prove that the nerves were in the 

 proper condition at any given time. Into such a tangled 

 maze of uncertainties are we led when we try to pervert 

 our senses, admirable in their proper sphere, into mechan- 

 isms for the quantitative estimation of energy ! 



If it be said that a single bell at the distance one will 

 sound as loud as four bells at the distance two, it must be 

 assumed that the ear is equally well adapted for receiving 

 and transmitting all sounds, irrespective of the shape cf 

 their wave front. I will omit from the following discus- 

 sion all the complications which spring from differences 

 in the pitch and timbre of sounds and will premise a per- 

 fect ear and nerves. 



According to the undulatory theory of sound, the wave 



