202 



SCIENCE 



[N. S. Vol. LIV. No. 1392 



1.7 8.2098 5.2 7.2844 



1.8 8.0378 5.3 6.8204 



1.9 7.8579 5.4 6.3479 



2.0 7.6700 5.5 5.8668 



2.1 7.4741 5.6 5.3771 



2.2 7.2702 5.7 4.8789 



2.3 7.0581 5.8 4.3721 



2.4 6.8379 5.9 3.8567 



2.5 6.6095 6.0 3.3328 



2.6 6.3730 6.1 2.8008 



2.7 6.1282 6.2 2.2593 



2.8 5.8751 6.3 1.7096 



2.9.... 5.6138 6.4.... 1.1514 



8.0 5.3442 6.5 0.5846 



3.1.... 5.0663 6.6.... 0.0092-20 



3.2 4.7800 6.7 9.4252-30 



3.3 4.4854 6.8 8.8326 



3.4 4.1824 6.9 8.2314 



3.5.... 3.8710-10 7.O.... 7.6216-30 



Percy W. Cobb 

 Laboratory op Ptjre Science, 

 Nela Eesearch Laboratories 

 May, 1921 



POLARIZATION OF SOUND 



The term polarization, applied to a wave 

 motion, is generally associated only with trans- 

 verse waves, more especially with light-waves, 

 as referring to a state in which certain quali- 

 ties are different in certain directions at right 

 angles to one another and to the direction of 

 propagation. By its origin, however, the term 

 may be used with the same justification for 

 longitudinal waves exhibiting qualities that 

 are different in different directions, irrespec- 

 tive of the nature of such qualities and the 

 relation of the various directions to each 

 other. 



It is thus proper to speak of a polarization 

 of sound when conditions prevail under which 

 a quality like its pitch is of opposite character 

 to opposite sides of a fixed plane or axis. 



Such conditions may be brought about by 

 putting the source, wliich for the sake of sim- 

 plicity is supposed to produce a sustained 

 sound of uniform pitch, through certain move- 

 ments. It is well known that when such a 

 source is in motion the pitch of the sound 

 emitted into space will be a function both 

 of the direction of the movement and its 

 speed. 



This is due to the relative displacement 

 of the individual wave rings by the motion, 

 and is readily observed by anyone standing 

 close to a railroad track while a locomotive 

 blowing its whistle is passing. At the in- 

 stant of passage there is a sudden fall in the 

 pitch of the blast, the fall being approximately 

 proportional to the speed of the locomotive. 



The pitch observed at any point may be ex- 

 pressed by the formula : 



p denoting the pitch observed, q the pitch 

 produced, v the velocity of sound, and u the 

 speed component of the movement in the di- 

 rection of the observer, with due consideration 

 of its sign. 



If the source, instead of being moved at 

 uniform speed in one direction, is made to 

 perform a harmonic oscillatory movement at 

 right angles to a plane P, and symmetrical to 

 it, then the resulting sound will be of uniform 

 pitch only at points located in this plane, as- 

 suming the extent of the movement to be small 

 as compared with the distance to the point of 

 observation. To either side of the plane the 

 pitch will be undulating, the undulations 

 reaching their maximum amplitude at points 

 directly in line with the movement. 



While the undulations will be of the same 

 amplitude at any two points symmetrically 

 located with respect to the plane, they will be 

 opposite in phase and, therefore, of opposite 

 character. Accordingly, if the source is made 

 to emit sound while to one side of the plane 

 only, i.e., during alternate half oscillations, 

 then, by the above formula, the resulting 

 sounds will be of descending pitch to that 

 side of the plane, while to the opposite side of 

 it the same sounds will be of ascending pitch. 



The sound may thus be said to have been 

 polarized with respect to the plane P. 



If the oscillatory movement of the source is 

 substituted by a rotation at uniform speed 

 about an axis A, results of a similar nature 

 are obtained. In this instance, however, the 

 resulting sound will be of uniform pitch only 



