106 Mr. Sudhansukumar Banerji on Aerial 



We thus arrive at the following results : — 



(1) The intensity of the sound varies as the square of the 

 change in velocity of the colliding spheres. 



(2) It varies inversely as the square of the distance from 

 the point of contact of the spheres. 



(3) It varies as the fourth power of the radius of the 

 spheres. 



The truth of these results has already been verified 

 experimentally, provided we assume that the apparatus 

 measures the intensity, which we shall presently see it 

 does. 



We can easily study the forced and the free vibrations 

 of the mica disk under the action of the sound-pulse. The 

 forced and free vibrations of a membrane and those of a 

 telephone plate have been studied by various writers^ 

 Without entering into mathematical details, we see that 

 the disturbance produced by impact travels forward as a 

 sound-pulse of the damped harmonic type which is sensible 

 only within a few diameters from the inner side of the 

 boundary of the advancing wave. Its action on the mica 

 disk, which has usually a smaller natural frequency of 

 vibration than that of the waves, is so very sudden and 

 lasts for so short a time that the whole effect partakes of the 

 character of an impulsive pressure in consequence of which 

 the mica disk suddenly acquires a velocity and free vibrations 

 of considerable amplitude are excited in it. Assuming that 

 the mica disk is not displaced considerably, we can easily 



see from elementary considerations that since p ~- is the 



pressure per unit area on the mica disk, where yjr is the 

 velocity potential of the sound-pulse and p the density of 

 air, the initial velocity communicated to the mica disk would 

 be practically proportional to the quantity 



[ P ^ dt , 



w 



t being the instant when the sound-pulse meets the mica 

 disk. When this velocity attains the maximum value, the 

 mirror leaves the pointer and moves with that maximum 

 velocity. This velocity is therefore proportional to the- 

 quantity [p^],, the instant t being so chosen that this 

 expression has the maximum value. If we denote this 

 quantity by v and the deflexion of the mirror by 0, then we 



