Sound- Shadows in Water. 99 



the boundaries of the sound-shadows are necessarily very 

 imperfectly denned; for the amount of difrractive divergence 

 proceeding from the secondary waves, originating at the 

 boundaries of the obstacle and propagated within the geo- 

 metrical shadow, is usually so considerable that the diminu- 

 tion of intensity of sound behind it, although quite perceptible, 

 is by no means so conspicuous as might be expected. 



3. The contrast, in this respect, between sound and light 

 is well expressed by Lord Rayleigh : — " When waves of sound 

 impinge upon an obstacle, a portion of the motion is thrown 

 back as an echo, and under cover of the obstacle there is 

 formed a sort of sound-shadow. In order, however, to pro- 

 duce shadows in any thing like optical perfection, the dimen- 

 sions of the intervening body must be considerable. The 

 standard of comparison proper to the subject is the wave- 

 length of the vibration ; it requires almost as extreme condi- 

 tions to produce rays in the case of sound, as it requires in 

 optics to avoid producing them " *. In other words, the dif- 

 ference between sound and light results from the well-known 

 fact, that an ordinary obstacle bears an immense ratio to the 

 length of a wave of light ; but does not bear a very great 

 ratio to the length of a sound-wave. Hence it follows, from 

 the mathematical theory of undulations, that the waves of 

 sound bend around obstacles, and produce more or less effect 

 within the geometrical shadow, whereas light-shadows have 

 definite boundaries and are more sharply defined. For, in 

 the case of light, calculation shows that at any point decidedly 

 within the geometrical projection of the obstacle from the 

 luminous source the disturbance vanishes, while at any point 

 outside of the geometrical projection the disturbance is the 

 same as if the primary wave had passed the screen unimpeded. 

 But this is only partially true in the case of ordinary sound- 

 waves, in consequence of their considerable length ; it is 

 rigorously true only when, as in optics, the diameter of the 

 obstacle is large in comparison with the wave-length. 



4. There are, however, other causes, depending upon the 

 differences between the sense of hearing and of sight, which 

 doubtless render the appreciation of the shadows of sound 

 much less distinct than those of light. On this point, Lord 

 Eayleigh justly remarks : — " In many cases sound-shadows 

 appear much less perfect than theory would lead us to expect. 

 The anomaly is due in a great measure, I believe, to an error 

 of judgment, depending on the enormous range of intensity 

 with which the ear is capable of dealing. The whistle of a 



* 'Theory of Sound,' vol. ii. p. 106, art. 283. London, 1:75. 



