of Difference of Phase of Sound- Waves. 457 



certain increase in phase-difference, the change o£ direction 

 increases regularly and uniformly. But when the phase- 

 difference becomes greater than f\, for \ = 64 cm., and 

 5X for \=104 cm., decision is more difficult, the apparent 

 direction remaining unchanged to some and to others the 

 angle is diminished. This may be shown by the following 

 summary : — 



When A = 64 cm., 



if 8<p is changed from to fX,— all but one noted a change in direction. 



., ,, ., £\ ., -}A,— ,, two ,. further increase in angle. 



i> 3* f eight noted a further increase in angle. 



I four .. a ., ,, ,, „ 



., .. .. |X .. £-X,— \ four .. no ., ,, „ „ 



[ two ., a decrease ,, ., 



n r ,. _ [five ., a further increase ,, ., 



"" "' ■' ' [five .. a decrease ., ., 



When X = 104 cm., 



if d<f> is changed from to 1 A,--all noted a change in angle. 



.. ., .. -i-X ., ^A,— ., ., a further increase in angle. 



f three noted a further increase in angle 

 ,, ,, ., }X ., {'A,— i three ,, no ., „ ,, „ 



! one ., a decrease ,, „ 



( two a further increase ,, ., 



|A „ |X,- J four no „ „ „ „ 



( one a decrease ,, „ 



We may then say, for the wave-lengths used, a phase- 

 difference up to about a quarter of a wave-length determines 

 partially or wholly the apparent direction o£ a sound. From 

 the properties of summation wave forms, we should expect a 

 difference of phase of a quarter wave-length to be the greatest 

 which would alter the form of the wave made by this addition. 

 The agreement between our observations and this property 

 of waves cannot, however, be said to be established except 

 for these wave-lengths, and experiments to test this point 

 should be made with sounds presenting great differences in 

 pitch. 



The experiments were continued up to a phase-difference 

 of a whole wave-length, and roughly for greater differences, 

 but the latter were not recorded as the angle continued, with 

 most observers, to be about 90°. 



Analytically, of course, the complex waves are identical 

 when the phase-differences of the component waves are zero 

 or a whole wave-length; and to explain the fact that most 

 observers noticed a difference in direction for these two 

 cases, we are led to believe that when one tube is so much 

 longer than the other, the intensity of the sound in the longer 

 tube then becomes appreciably less than in the other. This 

 supposition is supported by the fact that the majority found 



