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



Cor. — Since the maximum pressure in a transmitted vibra- 

 tion is 



and 



2ttA V 



— > 

 v 



y 



p=i-4n-. 



v 



The energy per second may then be written 



iPV. 



3. On the Reflexion of Sound at Gaseous layers of different 



Density*. 



We confine ourselves to the case of a cylinder, which we 

 suppose to be crossed by layers of gas of different density. 



Consider first one common surface, and let the velocity of 

 propagation on the side from which the air comes be v, on the 

 other side v' '. 



There will be generally a reflected and a transmitted dis- 

 turbance; let 



the amplitude of the incident disturbance be A, 

 „ „ reflected „ a, 



„ „ transmitted „ b. 



The common surface moves with the sum of the amplitudes 

 A, a of the one side, and with the amplitude b of the other ; 



.*. A + a = 5. 



The energy per second of A = that of a, b together ; 



{. V v v' J 



OYU V '~ X > A 2 = a 2 -f-^ 2 . 



Putting b 2 = (A + a) 2 , we find 



K\l-x) = a 2 (l + x) + 2kax\ 

 and, rejecting the solution A= — a, 6 = 0, we have 



* General formulae for a single surface were given by Green. The 

 object of this communication is chiefly to give an example of the method. 

 The case of oblique incidence loses most of its interest in practical appli- 

 cation to sound, as the necessary conditions for formal refraction are not 

 generally satisfied ; the investigation has been restricted to the simpler 

 case. 



