ECHOES OF BATS AND MEN 



the distance. Therefore, as the distance from bat to insect 

 increases, the net strength of the echo returning to the 

 animal's ears falls off as the fourth power of the distance. 

 If the insect is twice as far away, the intensity of its echo 

 is 1/2*, or l/16th as great. Let us suppose, for the 

 sake of argument, that a fishing bat does detect a small 

 fish at a distance of 10 centimeters. Since a fish's body is 

 acoustically similar to water, any echo it produces would 

 be most likely to come from the swim bladder. This is an 

 air-filled chamber which most small fresh-water fish have 

 within their bodies, and in a minnow it would be about 

 1 centimeter, or the same size as the insects detected in 

 air at 200 centimeters. If all other factors were equal, a 

 target at 10 centimeters would return an echo stronger 

 than one at 200 centimeters by a factor of (200/10)*, 

 or 1.6 X 10^. The two trips through the water surface 

 would reduce the fish echo by a factor of 1.33 X 10"^. 

 The product of these two numbers is 0.23, which would 

 mean that the echo received by the fishing bat under 

 these hypothetical conditions would have about one 

 fourth the intensity of the echo which is actually detected 

 by the bat catching insects in air. If this is really a vaHd 

 comparison, it puts the possibility of catching fish by 

 echoes in quite another light, since a factor of four is well 

 within the uncertainty of the assumptions I have made. 

 For example, the insect-catching bat may well detect 

 1 -centimeter insects at more than 200 centimeters, and 

 an increase in the distance of detection to 280 centi- 

 meters would produce an echo from the insect equal to 

 that from the hypothetical fish echo. 



This numerical argument, however, does not prove 

 that the fishing bats really do hear echoes from fish 

 through the water surface. It simply means that this pos- 

 sibility merits consideration and should not be rejected 

 out of hand because of the very large energy loss during 



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