ECHOES OF BATS AND MEN 



to the hill is not known and if the travel time of the 

 sound and its echo is a few seconds, a good stop watch 

 (which can measure time to a tenth of a second) would 

 allow us to determine the distance to the hill, if we as- 

 sume that we know the velocity of sound. Or if we know 

 the distance, we can use the same time measurement to 

 estimate the velocity at which the sound waves travel. 

 If the basic limit of accuracy in our time measurement 

 is determined by the stop watch at 0.1 second, the un- 

 certainty in our measurement of distance would be the 

 distance over which sound travels in that interval of 

 time, or approximately 34 meters. But this would be 

 the round-trip distance, so that theoretically we could 

 measure the distance to the hill with an accuracy of 

 ±17 meters. Another uncertainty is the human reaction 

 time, the interval between the actual arrival of a sound 

 and the pressing of the button on the stop watch. While 

 this is an appreciable fraction, certainly more than 0.1 

 of a second, there is not likely to be a great difference 

 between the first reaction time to the original sound and 

 the reaction time in stopping the watch when one hears 

 the echo; hence they will nearly cancel each other. An- 

 other error is likely to occur if the emitted sound and the 

 echo build up gradually. If a half second is needed to 

 reach maximum sound intensity, and if the echo is 

 enough fainter so that only the peak value is audible, 

 then we will probably find that the stop watch is pressed 

 one reaction time after the very beginning of the outgoing 

 sound, but not until one reaction time after the echo is 

 nearly at its peak. This can easily cause an error of about 

 0.3 second unless a very sharp sound is used for the ex- 

 periment. 



A similar experiment can be performed with the 

 clicker, provided it can be operated fairly rapidly. Sup- 

 pose you stand 30 meters from a large building and 



74 



