ECHOES OF BATS AND MEN 



Story, for searchlights, flashlights, and automobile head- 

 lights are all made more or less according to this prin- 

 ciple. But one of the important assumptions we have 

 made in this line of reasoning is that the sound waves 

 generated at the focus of a paraboUc horn really would 

 be reflected from the surface of the horn at an angle 

 equal to the angle of incidence. This is true only if the 

 wave length is short compared to the size of the reflecting 

 surface. K the wave length is much longer than the 

 dimensions of the horn, very little direction will be im- 

 parted to the sound waves. This means that a horn must 

 be several wave lengths in size to do what we want it 

 to do. What does this tell us about the frequencies of 

 sound that should be produced by an echo-generating 

 clicker? 



Suppose we decide to use 256 sound waves per sec- 

 ond. Since the velocity of sound is 344 meters per sec- 

 ond, this frequency corresponds to a wave length of 

 344/256, or about 1.3 meters. To be effective, our horn 

 must be several wave lengths in size, and even if it were 

 made of the Ughtest possible materials it would be un- 

 duly bulky. Clearly, then, we want short wave lengths 

 or high frequencies. But we cannot go to frequencies 

 above the upper limits of human hearing, which is 

 somewhere between 15,000 and 20,000 c.p.s. A good 

 compromise is about 5000 to 10,000 c.p.s. A wave 

 whose frequency is 10,000 c.p.s. has a wave length 

 of 344/10,000 meters, or a little under 3 centimeters. 

 It is quite practicable to build and carry a horn sev- 

 eral centimeters in size, and if this were the only 

 consideration we would choose the highest frequencies 

 or shortest wave lengths that were easily audible. Bats 

 use frequencies up to 130,000 c.p.s. with wave lengths 

 down to 2.5 millimeters, and their tiny mouths or ears 

 can concentrate these short sound waves quite effec- 



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