82 PLEASANT WA YS IN SCIENCE. 



it may grow louder or fainter according as the vibrations 

 increase or diminish in amplitude. But if the source of 

 sound is approaching the hearer, the waves are thrown closer 

 together and the sound is rendered more acute (the longer 

 waves giving the deeper sound) ; and, on the other hand, if 

 the source of sound is receding from the hearer, the waves 

 are thrown further apart and the sound is rendered graver. 

 The rationale of these changes is precisely the same as that 

 of the changes described in the preceding illustrations. It 

 might, perhaps, appear that in so saying we were dismissing 

 the illustration from sound, at least as an independent one, 

 because we are explaining the illustration by preceding illus- 

 trations. But in reality, while there is absolutely nothing 

 new to be said respecting the increase and diminution of 

 distances (as between the waves and corks of the preceding 

 illustration), the illustration from sound has the immense 

 advantage of admitting readily of experimental tests. It is 

 necessary only that the rate of approach or recession should 

 bear an appreciable proportion to the rate at which sound 

 travels. For waves are shortened or lengthened by approach 

 or recession by an amount which bears to the entire length 

 of the wave the same proportion which the rate of approach 

 or recession bears to the rate of the wave's advance. Now 

 it is not very difficult to obtain rates of approach or recession 

 fairly comparable with the velocity of sound about 364 

 yards per second. An express train at full speed travels, let 

 us say, about 1800 yards per minute, or 30 yards per second. 

 Such a velocity would suffice to reduce all the sound-waves 

 proceeding from a bell or whistle upon the engine, by about 

 one-twelfth part, for an observer at rest on a station platform 

 approached by the engine. On the contrary, after the engine 

 had passed him, the sound-waves proceeding from the same 

 bell or whistle would be lengthened by one-twelfth. The 

 difference between the two tones would be almost exactly 

 three semitones. If the hearer, instead of being on a plat- 

 form, were in a train carried past the other at the same rate, 

 the difference between the tone of the bell in approaching 



