SONAR AND RADAR 



and tape recorder so that the pulse was stored on tape. 

 Suppose that at some later time this recording was 

 played back into the water. The compression would oc- 

 cur during both reception and rebroadcast of the sound 

 waves, since in both cases the submarine would be mov- 

 ing relative to the water. Now suppose that the delay 

 between recording and playback is made less and less. 

 Nothing we do while shortening the delay time would 

 affect the compression of the train of sound waves, so 

 that there will still be two such compressions regardless 

 of whether the delay is long or short. If the delay is very 

 short, it approaches zero, and zero delay brings us back 

 to the original situation of immediate reflection. Thus 

 the porpoise hears the echo as 2000 waves occupying 

 only about 147 meters. To be sure, one can spUt hairs 

 and say that 150 X 149/150 X 149/150 X 149/150 are 

 a very little more than 147. But it is not much more, and 

 I promised to keep our arithmetic as simple as possible. 

 Finally the 2000 sound waves reach the receiving 

 hydrophone of the sonar ship, which is still advancing 

 at 10 meters per second to meet them, and the same 

 compression is repeated for the last time. The end re- 

 sult is that the receiving circuit of the sonar system gets 

 the 2000 waves in a shorter time than was required to 

 send them out. The amount of this shortening is 



149 

 0.1-0.1 ("jTfT^*' °^ approximately 0.03 second. 



The Doppler effect can be somewhat simplified by 

 considering only the relative motion of the sonar system 

 and its target; in this example the two were approaching 

 at 20 meters per second. The pulse length of the received 

 echo is then reduced by the square of the ratio of the 

 relative velocity of approach to the velocity of sound. 

 It is obvious that if the two ships were moving away 

 from each other, the Doppler effect would work in the 



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