324 



SCIENCE 



[Vol. LV, No. 1421 



figure 3, were obtained independently, one 

 after the other. 



Now in the line PP', normal to the wall W, 

 40 cm. above the table between pipe P and pipe 

 image P' in W, the nodes should follow each 

 other at a distance of 1/2 = 24 em. apart; but 

 as the distribution above and below is hyper- 

 bolic, the nodes at the level of the table must 

 be further apart. Unfortunately, the equation 

 is cumbersome. Without attempting to use it 

 here, we easily surmise that the increased dis- 

 tance so obtained is inadequate; i. e., not as 

 large as the 35 cm. intervals found in the 

 experiments, in place of X/2 = 24 cm. esti- 

 mated to increase to 27 cm. or 29 em. One 

 should expect 7 or 8 nodes in place of the 

 5 or 6 recognized. Thus it seems not unlikely 

 that a frequency of a near order is contributed 

 by the room itself, particularly as the reflected 

 waves returning from 2 meters are too weak to 

 compete effectively with the outgoing wave 

 trains. Furthermore, there is another wall in 

 the direction of negative y (at j/ = — 130) and 

 one at x =^ — 190 cm. Although apparatus lies 

 in the path here, they introduce further com- 

 plication. 



There remains the reflection from the table, 

 so that the pipe and its image 40 cm. below, 

 make the plane of the table a region of re- 

 enforcement; or, with regard to the loss of 

 X/2 at the surface, a locus of nodes, though 

 the term node would be strictly applicable only 

 for the ease of normal incidence near the line 

 pipe-image. The next nodal locus is hyperbolic 

 and therefore higher than 25 cm. above the 

 table, out of reach of the resonator which lies 

 on it. Thus it is finallj' necessary to compound 

 the phase reversed direct ray here in question, 

 with the corresponding phase reversed reflec- 

 tions from the walls, to get the disturbance at 

 any point of the table. This succeeds experi- 

 mentally, as I , will point out presently, for 

 walls close at hand (within a meter or two) ; 

 but for walls as distant as those of the room, 

 the reflection wall effect is too small to account 

 for variations as marked as those of figure 3. 

 It is possible that a wide high wall, like W , 

 may act obliquely bj' diffraction; but to speak 

 on this subject, further inquiry will be needed. 

 As a general fact, however, it is noticeable that 



a survey in y, between walls, here produces a 

 much more marked harmonic distribution of 

 acoustic pressure along that axis, than a sim- 

 ilar survey along x toward the open door (§4). 

 The strUiing opposition of phase which figure 

 3 presents for an inversion of the resonator is 

 more easily intelligible. As the length of the 

 resonator is approximately X/4, the rotation of 

 180° about its center will pass the mouth from 

 a node to a loop of the stationary wave train, 

 or between corresponding 90° phase differ- 

 ences. Now the pin hole probe, as above 

 stated, is sensitive to nodes (compressions) 

 only and scarcely responds to wave trains (or 

 to the similar harmonic motion at the loops). 

 The pin hole resonator might be thought to 

 have the opposed quality, being stimulated by 

 wave trains (or loops) and not by nodal 

 phenomena or compressions: but (§5) this 

 inference is not correct. We must therefore 

 again anticipate nodes at the maxima of the 

 graph and loops at the minima, when the pin 

 hole resonator is used. 



It folloAvs from this that if half of the 

 length of the resonator be added to the y co- 

 ordinate of one of the graphs, figure 3, and half 

 the length be deducted from the other, i. e., if 

 the mouth of the closed resonator be taken to 

 define the coordinate «/, the two curves of figure 

 3 should coincide at their mean position in y. 

 Hence if the resonator is rotated on an axis 

 passing through its mouth, the data obtained 

 should be constant at all angles. Experiments 

 were specially made to corroborate this infer- 

 ence. 



4. Survey {in x) toward the open door. The 

 example of this survey, which I will here 

 communicate, was made somewhat differently 

 from the preceding, by locating the resonator 

 at the origin (.■?; = j/ = ^ = 0) in two azimuths, 

 90° and 270°, successively. The pipe, kept 

 horizontal, parallel to y and 40 cm. above the 

 table, was now moved along the axis x. The 

 abscissas, d^, still refer to the distance between 

 the centers of the pipe and resonator, while 

 the coordinates x are marked in decuneters on 

 the curves. The graph then shows the effect 

 at the origin, of an f" pipe sounding at differ- 

 ent points along x, and the pressure distribu- 

 tion are here throughout quite different from 



