Note on the effect of wind pressure on the pitch of organ pipes
Henry Reginald Arnulph Mallock · Proceedings of the Royal Society of London Series A Containing Papers of a Mathematical and Physical Character · 1918
Abstract In books on acoustics the pitch of organ pipes is treated as being dependent solely on the length of the pipe, while at the same time it is recognised that, as a consequence of the conditions existing at the open end or ends, the length in question is somewhat greater than that of the pipe itself. The “correction for open ends” has been calculated for particular cases, and for the open end of a pipe of circular section amounts to an addition to its length of about 0·82 times the radius. The conditions at the base, or speaking end, are more complex, and for this (as far as I am aware) no similar correction has been worked out. For these reasons the natural pitch of an organ pipe cannot be accurately determined from its material dimensions, but only by experiment; such, for instance, as noting the frequency of an exterior source of sound which produces the maximum resonance in the pipe. When an organ pipe is made to “speak” in the ordinary way, it is a matter of common knowledge that the pitch of note produced is to some extent dependent on the pressure of the wind supply, and the fact (though often mentioned) has not been satisfactorily accounted for (Lord Rayleigh has published an accurate series of experiments on this subject, which will be referred to later.) The true explanation is exceedingly simple, but, like many other problems of the flow of fluids, it cannot, at present at any rate, be treated on a purely dynamical basis.