Condensational-rare factional Waves in Gases fyc. 495 



loud sound of the well-known musical character (C 2 56) will 

 be heard *. 



Increase the frequency now to 32 times this, that is to 8192 

 periods per second, and an exceedingly loud note 5 octaves 

 higher will be heard. It may be too loud a shriek to be 

 tolerable ; if so, diminish the range till the sound is not too 

 loud. Increase the frequency now successively according to 

 the ratios of the diatonic scale, and the well-known musical 

 notes will be each clearly and perfectly perceived through the 

 whole of this octave. To some or all ears the musical notes 

 will still be clear up to the G (24756 periods per second) of the 

 octave above, but we do not know from experience what kind 

 of sound the ear would perceive for higher frequencies than 

 25000. We can scarcely believe that it would hear nothing, 

 if the amplitude of the motion is suitable. 



To produce such relative motions of shell and nucleus as we 

 have been considering, whether the shell is embedded in air, 

 or water, or glass, or rock, or metal, a certain amount of 

 work, not extravagantly great, must be done to supply the 

 energy for the waves (both condensational and rarefactional), 

 which are caused to proceed outwards in all directions. Sup- 

 pose now, for example, we find how much work per second 

 is required (o main lain vibration with a frequency of 1000 

 periods per second, through total relative motion of 10~ 3 of a 

 centimetre. Keeping to the same rate of doing work, raise 

 the frequency to 10 4 , 10 5 , 10 6 , 10 9 , 10 12 , 500 x 10 12 . We now 

 hear nothing ; and we see nothing from any point of view in 

 the line of the vibration of the centre of the shell which I 

 shall call the axial line. But from all points of view not in 

 this line, we see a luminous point of homogeneous polarized 

 yellow light, as it were in the centre of the shell, with in- 

 creasing brilliance as we pass from any point of the axial line 

 to the equatorial plane, keeping at equal distances from the 

 centre. The line of vibration is everywhere in the meridional 

 plane, and perpendicular to the line drawn to the centre. 



When the vibrating shell is surrounded by air, or water, 

 or other fluid, and when the vibrations are of moderate fre- 

 quency, or of anything less than a few hundred thousand 

 periods per second, the waves proceeding outwards are con- 

 densational-rarefactionalj with zero of alternate condensation 



* Lord Rayleip-h has found that with frequency 256, periodic con- 

 densation and rarefaction of the marvellously small amount 6xl0~ 9 of 

 an atmosphere, or " addition and subtraction of densities far less than 

 those to be found in our highest vacua, ' gives a perfectly audible sound. 

 The amplitude of the aerial vibration, on each side of zero, corresponding 

 to this is 1-27x10-7 of a centimetre. — 'Sound/ vol. ii. p. 439 (2nd 

 edition). 



2 M 2 



