274 NEWTON S PRINCIPIA. 



repeated in the next interval, and so on throughout 

 all time. 



Thus we see a single pulse can be propagated along the 

 tube without any change in magnitude, form, or time of 

 vibration. In order to form these pulses let us imagine a 

 plate to be placed at one end of the tube, vibrating accord 

 ing to the law 



= a sin n t, 



then each pulse of the plate as formed will be propagated 

 unaltered along the tube, and the motion at any distance x 

 from the plate will be given by the law 



= a sin (n t m x). 



The velocity of sound is independent of the values of m 

 and n. These are the only constants on which the differ 

 ence between two notes could depend. Whatever, then, 

 is the pitch of a sound, it will travel with the same 

 velocity. 



The numerical value of the velocity of sound depends on 

 the constant K. This expresses the constant ratio of the 

 elastic force or pressure of the air to its density. The density 



of the air Newton calculated to be about th part of the 



j. io yu 



density of quicksilver, and the pressure of the air is equal 

 to the weight of a column of mercury about 30 inches 

 high. Hence the ratio of these two is equal to 



orj 



g x g x 11890, 



the units being feet and seconds of time. The square root 

 of this, which is the velocity of sound, is 979. Sound, 

 therefore, should travel at the rate of 979 feet per second. 

 The elastic force p for a given density being increased by 

 an increase of temperature, the result thus obtained should 

 be too small in hot air and too great in cold. But this 



