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On the Amplitude of Sound-waves. [May 31, 



II. " On the Amplitude of Sound-waves." By Lord Rayleigh, 

 M.A., F.R.S. Received May 3, 1877. 



Scarcely any attempts have been made, so far as I am aware, to mea- 

 sure the actual amplitude of sound-bearing waves, and, indeed, the pro- 

 blem is one of considerable difficulty. Even if the measurement could 

 be effected, the result would have reference only to the waves actually 

 experimented upon, and would be of no great value in the absence of 

 some means of defining the intensity of the corresponding sound. It is 

 bad policy, however, to despise quantitative estimates because they are 

 rough; and in the present case it is for many reasons desirable to have a 

 general idea of the magnitudes of the quantities with which we have to 

 deal. Now it is evident that a superior limit to the amplitude of waves 

 giving an audible sound may be arrived at from a knowledge of the energy 

 which must be expended in a given time in order to generate them, and 

 of the extent of surface over which the waves so generated are spread at 

 the time of hearing. An estimate founded on these data will necessarily 

 be too high, both because sound-waves must suffer some dissipation in 

 their progress, and also because a part, and in some cases a large part, 

 of the energy expended never takes the form of sound-waves at all. 



The source of sound in my experiment was a whistle, mounted on a 

 Wolf's bottle, in connexion with which was a siphon manometer for the 

 purpose of measuring the pressure of wind. This apparatus was inflated 

 from the lungs through an india-rubber tube, and with a little practice 

 there was no difficulty in maintaining a sufficiently constant blast of the 

 requisite duration. The most suitable pressure was determined by pre- 

 liminary trials, and was measured by a column of water 9^ centimetres 

 high. 



The first point to be determined was the distance from the source to 

 which the sound remained clearly audible. The experiment was tried in 

 the middle of a fine still winter's day, and it was ascertained that the 

 whistle was heard without effort at a distance of 820 metres. In order 

 to guard against any effect of wind, the precaution was taken of repeating 

 the observation with the direction of propagation reversed, but without 

 any difference being observable. 



The only remaining datum necessary for the calculation is the quantity 

 of air which passes through the whistle in a given time. This was deter- 

 mined by a laboratory experiment. The india-rubber tube was put into 

 connexion with the interior of a rather large bell-glass open at the bottom, 

 and this was pressed gradually down into a large vessel of water in such 

 a manner that the manometer indicated a steady pressure of 9| centi- 

 metres. The capacity of the bell-glass was 5200 cubic centimetres, and 

 it was found that the supply of air was sufficient to last 26^ seconds of 

 time. The consumption of air was therefore 196 cubic centimetres per 

 second. 



