Mr Sharpe, On the Reflection of Sound at a Paraboloid. 147 



different large values of p, then the magnification of sound 

 produced by the reflector varies as p%, so that if we suppose the 

 strength of source constant, the magnification would vary as p%. 

 Perhaps, remembering the linearity of the fundamental equation 

 of sound, we may put the last statement better thus. We have 

 proved that if we have in LO a source of sound whose total strength 



2% IT* 



= G x (where is a constant), 



p 



it will produce, at a distant point V, a velocity whose maximum 

 value 



But here we may put C = fip where fi is an arbitrary constant, 

 so that a source in LO, whose strength = /u, x 2^7r*, will produce 

 at Fa velocity 



= ,*(?? 026). 



This justifies the above statement about magnification. But 

 perhaps a still better measure of the sound magnification may be 

 arrived at by finding the ratio between the actual maximum 

 velocity given by (124) and what the maximum velocity at V 

 would be, if the reflector and source in LO were annihilated, and 

 there were at a singletree source whose strength is (123). We 

 shall find this ratio 



pV i 



4(2tt)*" 



We might adopt the coefficient of w * here as a fair measure of 

 the magnification. Whichever measure we adopt, we see that the 

 higher the pitch of the note (or tone) experimented on the greater 

 will be the magnification. 



11—2 



