Lord Rayleigh's Acoustical Observations. 157 



when the wind first comes on, the vibrations in the two 

 halves are similar, as is evidenced by the greater loudness ; 

 but the opposition of phase is rapidly established, usually in a 

 fraction of a second of time. As a system with two degrees 

 of freedom, the compound pipe is capable of two distinct 

 modes of vibration, in one of which the vibrations of the 

 component pipes are in the same phase, and in the other in 

 opposite phases. Why the action of the wind should maintain 

 the latter mode of vibration to the exclusion of the former 

 has not hitherto been explained ; but the fact remains that 

 that mode of vibration, which depends for its possibility upon 

 the barrier, is chosen in preference to the other mode, which 

 is not dependent upon the barrier, and in the absence of the 

 barrier is the one necessarily adopted. 



The two possible modes of vibration have, as in almost all 

 such cases, two distinct periods of vibration, the difference 

 depending upon the behaviour of the air just outside the 

 open ends. In consequence of the inertia of the external air 

 at an open end, the effective length of a pipe exceeds its 

 actual length by about six tenths of the radius. The in- 

 crement of effective length is therefore greater in the case of 

 the compound column of air when its parts vibrate in the 

 same phase, than it would be for either of the parts if removed 

 from the influence of the other. On the other hand, when 

 the vibrations are in opposite phases, the increment must be 

 much less, one component pipe absorbing the air discharged 

 from. the other. Accordingly one note of the compound pipe 

 is graver, and the other, which is the one actually sounded, is 

 more acute, than the natural notes of the component pipes 

 when supposed to act independently of one another. 



In order to show this effect it is not necessary that the two 

 pipes be similar, or even of exactly the same pitch. If two 

 pipes in approximate unison be placed so that their open ends 

 are contiguous, a mutual influence is exerted, which is usually 

 sufficient to prevent the production of beats. The examples 

 about to be given will show that the unison need not be 

 exact ; but the greater the deviation from unison, the more 

 intense is the residual sound. Beyond the limit of the ad- 

 missible departure from unison, beats ensue ; but at first 

 they are irregular, and liable to be disturbed by very slight 

 causes, such as draughts of air. According to theory, the 

 frequency of the beats ought to be a little greater than the 

 difference of the frequencies of the notes given by the pipes 

 independently ; but I have not been able to detect the difference 

 experimentally. It would therefore seem that over most of 

 the range for which the mutual influence is sensible and 



