130 THE UNIVERSITY OF OKLAHOMA 



within the atoms. Already the dreams of the ahhemists are coming 

 true, for nitrogen has been pounded to pieces by e'ectri:aiiy charged 

 atomic hammers, yielding sim.pler forms. When the h^^.-ivicr elements 

 can simularly be broken up the production of gold from lead may 

 be commonplace. 



It is interesting to recall that at that while 'i-e most minutf^ 

 divisions of matter are being studied by certain physicists, others 

 are measuring the diameters of the stars and Ein:.tein is asking us 

 to rearrange some of our most cherished ideas concerning time 

 and space. 



XXVill. THE CAUSE OF THE OPTIMUM ANGLT: IN A 



RECEIVING CONICAL HORN 



Victor A. Hoersch 



From the Physics Laboratory of the University of Oklahoma. 



Suppose that plane waves of constant amplitude and frequency 

 are incident upon the opening of a conical horn in the direction of 

 the axis of the horn. Let the length of the horn be adjusted foi 

 fundamental resonance to the incident waves. Let the amplification 

 of tlie horn be defined as the rafio of the amplitude of pressure 

 variation at the vertex of the horn to that in the incident plane 

 Vv'aves. We shall consider that the horn is u;ed as a receiver, in 

 which case there is an energy loss at the vertex. Neglecting the 

 energy loss due to the non-rigidity of the horn and that due to 

 the viscosity of the medium, the only other energy loss is that due 

 to the spherical waves radiated outwards from the opening of the 

 horn. 



Consider first the energy loss at rhe vertex. For horns of 

 different sized opening all in fundamental resouA.ice with the same 

 incident plane waves, the rate of loss of energy is proportional to 

 the square of the amplification and hence proportional to the square 

 of the energy input per unit area of the opening by the incident 

 waves. For horns of sufficiently small openings the energy radiated 

 from the open end can be neglected in comparison to that abstratod 

 at the vertex. In this case, in the steady state of vibration, when 

 the energy input equals the output, the energy input per unit area, 

 and hence the amplification, must be proportional to the area of 

 the openmg of the horn. 



Consider next the energy radiated at the open end of the 

 horn. For horns of different sized openings all in fundamental 

 resonance with the same incident plane waves, the rate of loss of 

 energy is proportional to tne square of the energy input. For horns 



