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126 PITCH AND LENGTH OF PIPE. [V. § 62.
Hence, the gravest tone obtainable from a stopped pipe is always one Octave lower than the gravest tone j>r >le from an open pipe of the same
length. It has been shown in § 39 that this result of theory is borne out by experiment.
62. In order to complete this investigation, it is necessary to determine the pitch of the lowest note which a pipe of given length is capable of uttering. By § 52 we know that a complete segmental vibration is performed during the time occupied by a pulse in traversing twice the length of a single seg ment. In (A) Fig. 39, this is equal to four times the length of the tube. The velocity of the pulse is here the velocity of Sound in air, which, under ordinary conditions of temperature, &c., we may put at 1125 feet per second1. The vibration-number of a stopped pipe's lowest tone is therefore found by dividing 1125 by four times the length of the pipe expressed in feet. Conversely the length of a stopped pipe which is to have as its deepest tone a note of given pitch, is found by dividing 1125 by four times the vibration-number of the note to be produced. The quotient gives the required length in feet. For example, middle C of the pianoforte makes 264 vibrations per second. The required length in this
1 Tyndall's Sound, p. 23.