ECHOES OF BATS AND MEN 



ample, a loud shout varies the air pressure by about 

 0.00001 to 0.0001 atmosphere, and the faintest sound 

 that can be heard by a normal human listener has pres- 

 sure variations of about 2 X lO'^^ (2/10,000,000,000) 

 atmosphere. 



People used to question the existence of sound in the 

 absence of a human listener. It was debated whether 

 there was any sound from a waterfall in the wilderness 

 when no one was there to hear it. This sort of question 

 ceases to be of much importance once one distinguishes 

 between the physical phenomenon of sound waves, pres- 

 sure changes which travel through the air, and the 

 subjective sensation of hearing a sound. The latter, of 

 course, requires a listener, although an animal would 

 do as well as a human being. But unless one believes 

 that the waterfall and the air around it have wholly dif- 

 ferent properties when no man is present, it is beyond 

 question that the physical sound waves are, in fact, gen- 

 erated as long as the water is falling. 



Sound waves travel in liquids and solids as weU as in 

 gases such as air, and while most of the time we will be 

 dealing with sound in air, we should bear in mind that 

 sound waves (that is, moving pressure changes) also 

 travel through the depths of the ocean or the hardest 

 steel. There is, however, one great limitation to the 

 travel of sound waves. They must have something to 

 travel through and they are barred forever from empty 

 space or from a perfect vacuum. Pressure results from 

 the coUisions of molecules with one another and with 

 whatever surfaces form the boundaries of a gas, liquid, 

 or solid. Sound can travel at appreciable intensities only 

 where appreciable pressures exist, and this means where 

 molecules are close enough together to collide with each 

 other reasonably often. 



The next important fact about sound waves is their 



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