ACOUSTICAL IXVESTIGATIOX OF HIE .lAPANESK BAMIJOO PIPE. 17 



slowly with d and then rapidly when d approaches the lialf wave 



length. The rapidity of the increase of the correction « with 



d, depends on the width of the lateral hole. Fig. 7. shows the 



relations between d and 'f, for Ci, corresponding to three different 



values of the diameter of the hole r. The curves have very long 



inflexions so that when d is neither very small nor near the half 



wave length, they may be regarded as approximately straight 



lines apparently converging to a point on the axis of d. 



For diöerent notes with different wave lengths, it was found 



that if the curves be drawn for different notes representing the 



relation of a and ■ (instead of (/), they coincide with each 



1 

 other very closely except when . is nearly I. This is true for 



holes with different areas. 



When d becomes greater than ~, the relation is quite similar 



to what it would be if the pipe were cut off at a distance equal 



to — from the open end. If the upper end of the pipe be 



perfectly closed by a rigid plate, the results are similar to those 



obtainable in case the pipe were prolonged by a length =^—0.4 R 



and the rigid j^lane were removed. If, again, the open end be 



partially closed with a plate having a circular hole, the case 



is quite similar to what it would be if the tube were produced by 



r — c where c is the correction of the length due to that partial 



opening. The latter fact has been verified experimentally with 



several mouth plates, with different diameters, the corrections 



due to which had been previously determined. Thus, « is periodic 

 with respect to -^, with the exact period of ■;. 



c) Several holes. 



When more than one hole is made, the case becomes much 

 comj^licated, since the different combinations of holes produce a 

 great number of cases wliich must be investigated inde[)en(lently. 



