MS Mr. R. H. M. Bosanquet on the Theory of Sound. 



The sum of these results =1, as it should be. In these 

 calculations it is supposed that the wave is of such length 

 compared with the thickness of the layer as to prevent inter- 

 ference-effects. 



Example. — Sound is transmitted across a layer of hydrogen ; 

 to find the energy per second transmitted and reflected. 



Density of hydrogen : density of air : : v 2 : v 12 : : 1 : 14*44 

 nearly ; 



whence v : v / : : 1 : 3*8 nearly. 



Calculating the above expressions, we find that, if energy 



per second of incident sound be taken as 1, it is divided as 



follows : — 



T . , , , 2 x 3-8 7-60 



Transmitted =1^44=15^ 



Reflected = (3'8-l) 2 _ 7-84 

 Kenected - 1 + u . u - u . u 



The transmitted and reflected energy are very nearly equal ; 

 and each is very nearly half that of the incident sound. 



We can find the value of v : v / for which the division should 

 be exactly equal between transmission and reflexion. 



Putting (v—v / ) 2 =2vv / , we find 



^=2± N /3 = 3'732 or -268, 

 v 



the one corresponding to passage from air through gas, the 

 other to the reverse. This value is within the limits marked 

 by the square root of the density and liegnault's determination 

 of the velocity in hydrogen. 



Regnault's determination. Square root of density. 

 3-682 3-801 



(These numbers are given correctly in Regnault, Mem. de 

 Vlnstitut, 1868, p. 135. They are accidentally transposed at 

 p. 553 of the memoir, and also in the summary in Tyndall, 

 2nd edit. p. 331.) 



As an illustration of the case where the wave-length is not 

 such as to prevent interference, suppose that we are dealing 

 with a layer of the thickness of a quarter wave-length in the 

 gas. Then each successive term of both transmissions and 

 reflexions is the opposite phase from that which precedes it, 

 so that the total energy transmitted is less than the above. 



The calculations, of which the above is an example, furnish 

 the explanation of Tyndall's observations about the acoustic 

 opacity of aerial layers of different density. 



The observation that the conditions of transmissibility are 



