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# Determination of the Vibration Frequency of a Note by a Siren

A siren is essentially an instrument for producing a musical note by a rapid succession of puffs of air. The simplest form of siren is a large circular cardboard disc, provided with perforations arranged in circles concentric with the disc. The puffs of air may be produced by blowing through a fine nozzle on to the circle of holes while the disc is maintained in rapid rotation. In order that the disturbances produced by the puffs of air passing through the holes may be periodic (see p. 164), the holes must be punched at equal distances from each other, and the disc must be driven at a uniform rate. If the pressure of the water-supply of the laboratory is sufficiently high, a small water-motor is a convenient engine for driving the disc, which must be mounted on an axle with a driving pulley. If the diameter of the disc is considerable, so that a large number of holes can be arranged in the circle, a rotation of the disc giving four revolutions per second is quite sufficient to produce a note of easily recognisable pitch. The revolutions in a given interval, say, one minute, can be counted, if a pointer be attached to the rim of the disc, and arranged so that it touches a tongue of paper fixed to the table once in every revolution. The number of taps on this paper in a given time is the number of revolutions of the disc. Suppose the number of taps in one minute is N, and the number of holes in the circle which is being blown is n, then the number of puffs of air produced per minute is Nn, and hence the number, per second is Nn/60.

The disc is generally provided with a series of concentric rings of holes differing in the number of perforations in the circle, so that a variety of notes can be blown for the same rate of rotation of the disc.

In the more elaborate forms of the instrument a metal disc, which is perforated with holes arranged in concentric circles, is mounted on a spindle so that it can revolve parallel and very near to the lid of a metallic box, which can be supplied by air from foot-bellows. The lid of this box is perforated in a manner corresponding to the revolving disc, but the holes in either opposing plate, instead of being bored perpendicularly through the metal, are made to run obliquely, so that those in the upper disc are inclined to those in the lower. When air is driven through the box it escapes through the holes, and in so doing drives the disc lound. The disc may thus be maintained in a state of rotation, and if the pressure of the air be maintained constant the rotation will be uniform. In driving the siren a pressure-gauge, consisting of a U-tube containing water should be in connection with the tube conveying the air from the bellows to the instrument; the blowing should be so managed as to keep the pressure of wind as indicated by this gauge constant

The number of revolutions of the spindle carrying the revolving disc is generally indicated on two dials - one showing revolutions up to a hundred, and the other the number of hundreds - by a special counting arrangement. This arrangement can be thrown in and out of gear at pleasure, by pushing in one direction or the opposite the knobs which will be found either in front or at the sides of the box which carries the dials.

The process of counting the revolution of the spindle is then as follows: - First read the dials, and while the rotation is being maintained constant by keeping the pressure constant, as indicated by the gauge, throw the counting apparatus into gear as the second hand of a watch passes the zero point; throw it out of gear after a minute has been completed, and read the dials again. The difference of readings gives the number of revolutions of the spindle in one minute; dividing by 60 the number per second is obtained.

To obtain the number of puffs of air we have to multiply by the number of holes in the revolving circle. In the modification of the siren by Dove there is a series of circles of holes, which can be opened or shut by respectively pushing in or pulling out plugs in the side of the box. The number of holes in the circles opened or shut by the respective plugs is stamped on the head of the plugs themselves.

In Helmholtz's double siren(1) we have practically two siren discs working on the same spindle; the box of one of the sirens is fixed, while that of the other is capable of comr paratively slow rotation. By shutting off all the holes of the one box this siren can be used exactly as a single one.

We are thus furnished with a means of producing a note of any pitch, within certain limits, and of counting at the same time the number of puffs of air which are required to produce it. The note produced by a siren is not by any means a pure tone; the upper partials are sometimes quite as loud as the fundamental tone.

To measure the vibration frequency of a note by means of the siren, the pressure of air from the bellows must be adjusted so that the siren is maintained at a constant rate of rotation, and giving out a note whose fundamental tone is in unison with that of the given note, one circle of holes alone being open. The condition of unison between the two notes may be attained by starting with the siren considerably below the necessary speed, and, sounding the note at same time, gradually increase the speed of the siren until beats are distinctly heard between the given note and the siren. As the speed of the siren is still further urged the beats become less rapid until they disappear; the blower should then keep the pressure so constant that the note of the siren remains in exact unison with the given note, and while this constancy is maintained a second observer should measure the rate of rotation of the spindle. The beats which will be heard if the note of the siren is too high or too low serve to aid the blower in controlling the note of the siren. Suppose that the number of revolutions per minute is N, and the number of holes in the open circle n, then the vibration frequency of the note is Nn/60.

The method of procedure with the simpler siren previously described is similar. The speed of rotation depends in that case, however, on the rate of driving of the engine; the experiment is therefore somewhat simpler, although the range of notes obtainable is rather more limited. The speed can be controlled and kept steady by subjecting the driving string to more or less friction by the hand covered with a leather glove.

Care should be taken not to mistake the beats between the given note and the first upper partial of the note of the siren, which are frequently very distinct, for the beats between the fundamental tones.

The result of a mistake of that kind is to get the vibration frequency of the note only half its true value, since the first upper partial of the siren is the octave of the fundamental tone. It requires a certain amount of musical perception to be able to distinguish between a note and its octave, but if the observer has any doubt about the matter he should drive the note of the siren an octave higher, and notice whether or not beats are again produced, and whether the two notes thus sounded appear more nearly identical than before.

The most convenient note to use for the purpose of this experiment is that given out by an organ-pipe belonging to the octave between the bass and middle C's. In quality it is not unlike the note of the siren, and it can be sounded for any required length of time. For a beginner a tuning-fork is much more difficult, as it is very different in quality from the siren note, and only continues to sound for a comparatively short time.

If a beginner wishes to find the vibration frequency of a fork by the siren, he should first select an organ-pipe of the same pitch. This can be tested by noticing the resonance produced when the sounding fork is held over the embouchure of the pipe. Then determine the pitch of the note of the organ-pipe by means of the siren, and so deduce that of the fork.

Experiment. - Find the vibration frequency of the note of the given organ-pipe.

Enter results thus:

Organ-pipe - Ut. 2.

(1) By the Helmholtz siren:

Pressure in gauge of bellows, 5 inches.

Revolutions of spindle of siren per minute, 648.
Number of holes open, 12.
Frequency of note, 129.