ECHOES OF BATS AND MEN 



2000 sound waves altogether. Let us simplify our arith- 

 metic by assuming that the velocity of sound in sea water 

 is exactly 1500 meters per second. If the ship were 

 stationary, the pulse would occupy 1500 X 0.1, or 150 

 meters of distance through the water. But it is moving 

 at 10 meters per second, or 1 meter in the one tenth 

 second required to emit the 2000-wave pulse. Since the 

 transmitting hydrophone pursued the sound waves and 

 covered 1 meter while emitting the pulse, the train of 

 waves was thereby compressed into 149 meters instead 

 of 150. This does not affect the velocity of sound in sea 

 water, so that a passing porpoise would hear the pulse 

 as 2000 waves occupying 149 meters and traveling like 

 all other sound waves at 1500 meters per second. All 

 the waves of the pulse strike the porpoise in 140/1500, 

 or 0.099 second, and their frequency would therefore 

 be 2000 waves in 0.099 second, or 20,202 c.p.s. In 

 other words, the emitted pulse has a higher frequency 

 to the listening porpoise because the ship has moved 

 during the process of emitting it. The velocity of sound 

 depends entirely upon the medium in which it is travel- 

 ing, not upon the velocity of the sound source. 



Let us carry our example a little further and suppose 

 that this pulse strikes a submarine which is moving 

 west, toward the sonar ship, also at 10 meters per sec- 

 ond. The pulse, which was 149 meters long as it passed 

 the porpoise, is further compressed during the 0.1 sec- 

 ond while it is coUiding with the oncoming submarine. 

 As it is bouncing back from the target, it is again com- 

 pressed, both times by the same factor of 149/150. It 

 is not necessarily easy to see why this compression oc- 

 curs twice on striking the submarine, but an imaginary 

 modification of the physical events may help. Suppose 

 that the submarine did not return the echo by immediate 

 reflection but rather was equipped with a hydrophone 



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