Comparing Tuning-forks

To compare the Frequencies of two Tuning-forks of nearly Identical Pitch, and to tune two Forks to unison.

A tuning-fork mounted upon a resonator - a wooden box of suitable size - furnishes a very convenient means of obtaining a pure tone; the upper partials, which are generally heard when the fork is first sounded, are not reinforced by the sounding box, and rapidly become inaudible, while the fundamental tone is, comparatively speaking, permanent. When two forks which differ only slightly in pitch are set in vibration together, the effect upon the ear is an alternation of loud sound with comparative silence. These alternations are known as beats, and they frequently are sufficiently well marked and sufficiently slow for the interval of time between successive beats to be determined with considerable accuracy by counting the number occurring in a measured interval of time.

It is shown in text-books on sound⁽¹⁾ that the number of beats in any interval can be inferred from the vibration numbers of the two notes sounded together, and that, if N be the number of beats per second, n, n' the frequencies of the two notes, n being the greater, then

We have, therefore, only to determine the number of beats per second in order to find the difference between the frequencies of the two notes. This may be an easy or a difficult matter according to the rapidity of the beats. If they are very slow, probably only few will occur during the time the forks are sounding, and the observer is liable to confuse the gradual subsidence of the sound with the diminution of intensity due to the beats. If, on the other hand, there are more than four beats per second, it becomes difficult to count them without considerable practice. The difficulty is of a kind similar to that discussed in the section on rating a watch, and we may refer to that section for further details of the method of counting.

In order to determine which of the two forks is the higher in pitch, count the beats between them, and then lower the pitch of one of them by loading its prongs with small masses of sheet lead, or of wax (softened by turpentine), and observe the number of beats again. If the number of beats per second is now less than before, the loaded fork was originally the higher of the two; if the number of beats has been increased by the. loading, it is probable that the loaded fork was originally the lower; but it is possible that the load has reduced the frequency of the higher fork to such an extent that it is now less than that of the unloaded second fork by a greater number than that of the second was originally less than that of the first. It is safer, therefore, always to adjust the load so that its effect is to diminish the number of beats per second, that is, to bring the two forks nearer to'unison; to do so it must have been placed on the fork which was originally of the higher pitch.

In order to adjust two forks to unison, we may lower the pitch of the higher fork by weighting its prongs until the beats disappear; the difficulty, already mentioned, when very slow beats are observed occurs, however, in this case, and it is preferable to use a third auxiliary fork, and adjust its pitch until it makes, say, four beats a second with that one of the two forks which is to be regarded as the standard, noting whether it is above or below the standard. The second fork may then be loaded so that it also makes four beats a second with the auxiliary fork, taking care that it is made higher than the auxiliary fork if the standard fork is so. The second fork will then be accurately in unison with the standard - a state of things which will probably be shown by the one, when sounded, setting the other in strong vibration, in consequence of the sympathetic resonance.

A tuning-fork may be permanently lowered in pitch by filing away the prongs near their bases; on the other hand, diminishing their weight by filing them away at their points raises the pitch. Such operations should, however, not be undertaken without consulting those who are responsible for the safe custody of the forks.

Experiment. - Compare the frequencies of the two given forks A and B by counting the beats between them. Determine which is the higher and load it until the two are in unison.

Enter results thus:

Number of beats in 25 secs	67
Number per sec.	2.7
Number per sec. (A loaded)	3.3
Number per sec. (B loaded)	2.1
B is the higher fork.
Number of beats per sec. between A and the auxiliary fork C	3.6
Number of beats per sec. between B (when loaded) and the auxiliary fork C	3.6

(1)	Deschanel, Natural Philosophy, p. 813; Stone, Elementary Lessons, p. 72; Tyndall, On Sound, p. 201.