ECHOES OF BATS AND MEN 



short, there are more of them in a given distance and 

 more reach a given point in any particular interval of 

 time, which is another way of saying they have a higher 

 frequency. Expressed as a simple equation, velocity 

 equals frequency times wave length (v = fxX). Or 

 since the velocity is always the same under a given set of 

 conditions, the wave length varies inversely as the fre- 

 quency. A sound wave having a frequency of 344 waves 

 or cycles per second has a wave length of approximately 

 1 meter; 1376 c.p.s. has a wave length of 0.25 meter, 

 and a wave length of 2 centimeters (0.02 meter) cor- 

 responds to a frequency of 344 ^ 0.02, or 17,200 cycles 

 per second. High frequencies are often expressed in 

 kilocycles (thousands of cycles) per second, abbreviated 

 kc. A sound lasting 1 second, whatever its frequency 

 may be, extends 344 meters from start to end as it 

 travels through the air. A cUck lasting only 1/1 00th 

 second is 3.4 meters from front to back. And a sentence 

 which takes 10 seconds to utter would extend 3440 

 meters (more than two miles) from the speaker's mouth 

 if his voice were strong enough to carry that far. Assum- 

 ing that the atmosphere is dense enough to carry sound 

 waves up to an altitude of only 30,000 meters and your 

 voice loud enough, it is amusing to estimate how long a 

 sound would have to last in order to make a continuous 

 series of sound waves from your mouth up to 30,000 

 meters. It would be 30,000/344 or about 87 seconds, 

 or 1.5 minutes, roughly the time it would take you to 

 read aloud half a page from a book. 



The interactions of sound waves with ourselves and 

 the objects around us are less obvious than those involv- 

 ing light. For example, almost every solid object casts 

 some sort of shadow if exposed to light shining from 

 one direction. But most famihar sounds can be heard 

 with little change if the same shadow-casting object is 



42 



