ECHOES OF BATS AND MEN 



incidence. But quite different results are observed if the 

 object reflecting the waves is only one wave length or 

 less. Then one sees secondary waves which may be called 

 echoes radiating in many directions from the small ob- 

 ject. The strength of the echo waves in different direc- 

 tions varies in a complicated way, both with the shape 

 of the object and particularly with its size, relative to 

 the wave length. In fact, if the object is much smaller 

 than one wave length, its shape makes almost no differ- 

 ence at all. Later on I shall describe some simple experi- 

 ments with the clicker by which one can see how these 

 same rules apply to audible sound waves. When the ech- 

 oes travel in many directions from an object which itself 

 is small compared to the wave length, they are often 

 called scattered rather than reflected sound. 



But we started this digression to consider how the 

 wave length of the click would affect the usefulness of a 

 horn to direct the sound straight forward. A horn is a 

 special kind of acoustic mirror, and for this purpose we 

 want one shaped so that sound waves generated some- 

 where inside will all be reflected from the horn's surfaces, 

 reinforcing each other and coming out of the mouth 

 as parallel wave fronts traveling in the same direction. 

 If the sound is generated at a point, the most effective 

 horn to concentrate the sound waves into one direction 

 will be one with a parabolic shape. This means that if 

 you cut the horn longitudinally, any section will be a 

 parabola with the sound source at its focus. One of the 

 geometrical properties of a parabola is that any line 

 radiating from the focus will strike the surfaces of the 

 parabola at such an angle that when reflected (at an 

 angle equal to the angle of incidence) it will be parallel 

 to the axis of the parabola. 



This sounds rather complicated, but perhaps Fig. 8 

 will help to make it clear. Really this is a very familiar 



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