248 DYNAMICAL THEORY OF SOUND 



case of a grating formed by equidistant bars of circular section, 

 the corresponding value of / is 



l=7rb*/a, (8) 



where b is the radius of the section, and a the distance between 

 the axes of consecutive bars. It is implied, however, that the 

 ratio b/a must not exceed (say) J. 



83. Contrast between Diffraction Effects in Sound and 

 Light. Influence of Wave-Length. 



In the investigation of 82 an aperture was found to act as 

 a simple source from which sound diverges on the farther side 

 uniformly in all directions. This is in striking contrast with 

 what is usually observed in the case of light. We have so far 

 no indication of anything of the nature of beams or rays of 

 sound, just as when sound waves were incident on an obstacle 

 we found nothing of the nature of a sound-shadow. The 

 difference in the results is due to the fact that the dimensions 

 of the aperture (or obstacle) have been supposed small in 

 comparison with the wave-length, whereas with light the 

 relation is usually the reverse. 



We have avoided trespassing on the domain of Optics, but 

 as the dynamical conditions are in the present subject perfectly 

 definite, it may be permissible to examine this question of the 

 influence of wave-length a little more fully. 



Consider the region of space lying to the right of the plane 

 x = 0. If this plane were a fixed boundary, and if there were 

 no sources of sound in the region, any disturbance would 

 ultimately pass away. Any steady periodic motion in the 

 region must therefore in the absence of internal sources be due 

 to motion of the boundary, and will be determinate when the 

 value of the normal component of the velocity at every point of 

 the latter is given. It can, moreover, be expressed in terms of 

 this distribution of normal velocity, as follows. The flux out- 

 wards from an element 8$ of the plane is d<f>/dn . &S, if &n 

 denote an element of the normal drawn inwards from &S, and 

 if in imagination we associate with this an equal flux in the 

 opposite direction on the other side, the result is equivalent 



