268 ME. C. J. T. SEWELL : EXTINCTION OF SOUND IN A VISCOUS ATMOSPHERE 



If the radius of each obstacle is measured in centimetres, then the reciprocal of a, 

 as determined by (4), will give the distance travelled by the sound before its intensity 

 is diminished in the ratio of 1/e. If the radius of each small sphere is 1CT 3 cm., and 

 there are 10 6 per c.cm., then %mra? will be a small fraction, and the formula (4) will be 

 applicable. With these numerical values we obtain, in the case of sound of wave- 

 length 50 cm., = 8'5 10~ 2 . Consequently a" 1 = 11'8 cm.; hence, after passing 

 through a thickness of less than 12 cm. of such a medium, the intensity of the 

 sound will be diminished in the ratio of 1/e. 



The formula (4) should be applicable to fogs, as we may regard the water particles 

 as approximately fixed, since their inertia is so much greater than that of the 

 surrounding air. I am indebted to Prof. LAMB for the following information from 

 H ANN'S ' Meteorologie ' : " In a dense fog the amount of water may vary from about 

 3 to 10 gr. per cubic metre. Assuming that the diameter of the drops is '02 mm., 

 and a cubic metre contains 4'5 gr. of water, this is calculated to give 10* drops per 

 cubic metre, and therefore 10 3 per cubic centimetre." With these numerical data the 

 formula (4) gives a" 1 = 1180 metres, and consequently it follows that the fog would 

 not interfere appreciably with the propagation of sound. But if the diameter of the 

 drops could be as small as '002 mm., a fog of the same density would contain 10" 

 drops per cubic centimetre, and "' would be nearly equal to 1^ metres, and 

 consequently the sound would be damped very quickly by the fog.* On the other 

 hand, TYNDALL'S observations appear to show that the presence of fog is not 

 prejudicial to the audibility of sound, t 



The coefficient of sin (hx + a-t) in (3) gives the refractivity of the medium as 

 modified by the spherical particles. If 8 be the retardation due to the spheres of 



the stratum dx, 



8 = ln7r.c/.r. 3 ( + 3 v /2X-V^ 1 ). 



Hence, if p be the refractive index of the medium as modified by the particles, 



where p denotes the ratio, assumed small, of the volume occupied by the particles to 

 the total volume. 



Hence finally we have 



M ........ (5). 



For sound of wave-length 50 cm. incident upon a medium in which there are 10* 

 spherical particles per cubic centimetre, each of radius 10~ 3 cm., we obtain 



/*-! = 3.7.10" 2 . 



* See, however, note at end. 



| EAYLEIGH, ' Treatise on Sound,' Vol. II., p, 137. 



