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106                    HAND-BOOK OF ACOUSTICS.
reaching the stopped end, is reflected unaltered. Now the closed end of a stopped pipe must always be a node, since no longitudinal vibrations of the air particles can occur there; and as we have seen above, the open end must be the middle of a ventral segment, therefore the simplest form in which the air column in a stopped pipe can vibrate, is that represented in (A), fig. 56. This form of
Fig. 56.
vibration must therefore produce the fundamental tone of the pipe. Comparing it with the simplest form in which the air in an open pipe can vibrate, A, fig. 54, it will be seen that the open pipe has two half segments, while the stopped has only one ; consequently, if the pipes be of equal length as represented, the vibrating segment of the latter is twice as long as the former. Hence, as we have already seen, the fundamental tone of a stopped pipe, is an octave lower than that of an open one of the same length.