He showed, both by analysis and by synthesis, that quality depends on the order, number and intensity of the overtones or harmonics that may, and usually do, enter into the structure of a musical tone.
A " stopped pipe " in an organ is a pipe of this type, and both the fundamental and the overtones may occur simultaneously when it is blown.
The whole series of fundamental and overtones gives the complete set of harmonics of frequencies proportional to 1, 2, 3, 4, ..., and wave-lengths proportional to 1, 2, 3, 4 ..
It is evident that the overtones will follow the same rule as for a pipe opened at both ends.
But keeping r/X small we may as before form stationary waves, and it is evident that the series of fundamental and overtones will be just as with the air in pipes, and we shall have the same three types - fixed at one end, free at both ends, fixed at both ends - with fundamental frequencies respectively 41, p ' 21 V p, and I velocity in rod =velocity in air X distance between dust heaps.