ON ACOUSTIC PRESSURE AND

ACOUSTIC DILATATION

1. Introductory. Apparatus.-On a number of occasions, heretofore1 I have endeavored to use the interferometer for the measurement of Mayer and Dvorak's phenomenon: but though the experiments seemed to be well designed and were made with care, they invariably resulted in failures. The present method, however, has been successful and led to a variety of results.

The apparatus is shown in Fig. 1, where B is a mercury manometer described elsewhere, the displacements being read off by the component rays LL' of the vertical interferometer. The mercury of the U-tube is shown at m n m', above which are the glass plates g, g', the former being hermetically sealed, the latter loose, so that the air has free access. The closed air chamber R above m, receives the air waves from the plate of the telephone T by means of the quill tubes t hermetically sealed into the mouthpiece of the telephone, and sealed into the manometer. Finally t" is a branch tube ending in a small stopcock C or similar device at one end, while the other communicates with tt'. Flexible rubber tube connectors may be used at pleasure, so long as the space bounded by the outer face of the telephone plate, the mercury surface m and the stopcock C is free from leaks.

The cock C will eventually be replaced by the glass tubes c and c' (enlarged) perforated with minute orifices at O at one end and open at the other.

The telephone is energized by two storage cells and a small inductor with a mercury or

1 Carnegie Publ., No. 149, part III., pp. 206-08, Washington, 1914, and subsequently. The phenomenon has been studied by Rayleigh, Kolacek, Lebedew, Wien, Geigel and others. As to hydrodynamic forces in pulsating media, the researches of Bjerknes and W. König should be mentioned.

The displacements of the achromatic fringes corresponding to the head of mercury in B may be read off by a telescope provided with an ocular .1 mm. micrometer. It is perhaps advantageous to place the micrometer in the wide slit of the collimator, the fringes being parallel to the scale parts. To obviate the need of adjusting the inclination of the fringes (as this frequently changes), the slit holder should be revolvable around the axis of the collimator, the scale being parallel to the length of the slit and the fringes moving in the same direction across the white ribbonlike field. Fringes equal to a scale part in breadth are most convenient.

2. Observations. Closed and Open Resonators.-Spring interruptors dipping in mercury were first used, having frequencies of n=12 and 100 per second, respectively.

7

log n→→ f' g' a' c" d" e" g" a".

=

logn→→

gra

α

Since for sss the head is sλ/2 (the displacement being a fringes of wave-length A), this mean value, s=7 fringes for the given intensity of vibration, is at once equivalent to Ap=2 X 10-4 cm. of mercury, or to about 3 X 10-6 atmosphere. If but 500 ohms are put into the telephone circuit, however, appreciable deflection ceases.

Again, if the stopcock C is completely open no effect whatever is obtained. The bore of the small stopcock in this case need not exceed 2 or 3 mm. All the negative results which I obtained by other methods heretofore are thus explained.

found to increase from zero, with great rapidity to a positive maximum. The deflection then falls off with similar rapidity through zero to the negative value when the cock is again quite closed. I have indicated this result graphically in Fig. 2, in which the abscissas show the degree to which the cock has been opened and the ordinates the fringe deflections, 8, obtained. The maximum pressure obtained in these initial experiments was the equivalent of about 50 fringes; i.e., Ap=1.5 X 10-8 cm. or about 2 X 10-5 atmosphere for a frequency of about 12 per second. At higher frequencies this datum is much increased.

These pressures are real: for on suddenly closing the cock at the maximum and breaking the current, they are retained until discharged on opening the cock.

4. Pressure Depending on the Frequency and on the Intensity of Vibration.-The maxima are observable for very considerable reductions of the intensity of vibration. In Fig. 3 curves 3, 5, I have given examples of the observed fringe displacement, s, when different resistances (given by the abscissas in 10 ohms) are put in the telephone circuit. In curve 3 the frequency is n = 12 per second. Curve 5 contains similar results when the frequency is n=100 per second. The sensitiveness has obviously greatly increased and in a general way this is the case for higher frequencies.

5. Fringe Deflection Varies as Current Intensity. The graphs, Fig. 3, are roughly hyperbolic, so that the equation rs = C (r being the high resistance inserted into the telephone circuit) may be taken to apply within the errors of observation for resistance exceeding 1,000 ohms. So computed for convenience rs is 24 X 103 in series 3 and 36 X 103 in series 5. Hence at r 100 ohms the pressure would have been 7X 10-8 and 1.1 X 10-2 cm. of mercury. The instrument taken as a dynamometer is thus noteworthy, since its deflections would vary as the first power of the effective current or iis. It is of interest, therefore, to ascertain how far the sensitiveness which can not here be estimated

as above 10-4 amperes per fringe, may be increased.

6. Pin Hole Sound Leaks.-Pin holes less than a mm. in diameter seem more like a provision for light waves, than for sound waves often several feet long; but one may recall the phenomenon of sensitive flames.

It is so difficult to make the fine adjustment for maximum conditions with stopcocks that their replacement by the devices given in c and c', Fig. 1, is far preferable. Here c is a quill tube, to one end of which a small sheet of very thin copper foil has been fastened with cement. The sound leak at O is then punctured with the finest cambric needle. The other end (somewhat reduced) is thrust into a connector of rubber tubing at t". In case of c' the tube has been drawn out to a very fine point. This is then broken or ground off until the critical diameter (.04 cm.) is reached. Both methods worked about equally well but in the case c several holes side by side or holes of different sizes may be tried out. Such results are shown in Fig 4, which exhibits the deflection (s fringes, ordinates) for different diameters of hole in mm. (abscissas), when 1,000 ohms were put in the telephone circuit. It will be seen that the optimum .4 mm. in diameter is quite sharp. The finest size of needle is needed.

An example of results obtained with the sound leak c when different resistances are in circuit, is given in Fig. 3, curve 8. The value of rs; viz.,

phone sounds, pressure increments may even become negative, as above. If most of the water is removed by bibulous paper a moderate fairly constant pressure is usually observed for some time, until (doubtless with the breaking of the film across the hole) the maximum is suddenly again attained.

7. Inside and Outside Stimulation.-When the tube c' is inserted within the rubber connectors t, t' in the absence of vents, there is much undesirable pressure disturbance at the outset, which is but very slowly dissipated. Moreover the closed space can not be opened again at pleasure without similar commotion. I, therefore, used the apparatus, Fig. 6, in preference, in which the pinhole tube c' is provided with a branch tube t" and cock C. The rubber tube t leads to the telephone (beyond T) and the tube t' to the mercury U-tube (beyond U). If C is open, c' may be inserted or withdrawn with facility. If C is closed the resonator R is closed, as in the above case.

Using the mercury interruptor (frequency c) with 2,000 ohms in circuit the deflection of the closed region was invariably negative. The deflection is peculiar, moreover, inasmuch as it is a slow growth within a minute or more, to a maximum. On breaking the current the deflection dies off in the same slow fluctuating way. If the cock C is opened, the zero is instantaneously recovered. In other words the dilation is due to a loss of gas within the closed region, which loss is but slowly restored after the telephone ceases to vibrate.

If the cock C, Fig. 2, is opened at the critical point, or if it is replaced by the tube c, the deflection is again positive. The action of c thus exceeds that of c', probably because the pinhole in c happens to be nearer the critical size than in c'.

The question next at issue is the influence

f" g" pitch

200 35 0 fringes

There is thus an enormous maximum dilatation somewhere in the range of frequency d", e", which from the hovering character of the deflection is not further determinable. This amounts to a pressure decrement of Ap-6X 10-3 cm. of mercury with 2,000 ohms in the telephone circuit. At 100 ohms it would have been about a millimeter of mercury.

The slow growth of relatively enormous pressure decrements here recorded is so surprising that further experiments are needed. To begin with one may ask whether the telephone plate, held as usual by strong screw pressure between annular plates of hard rubber, is adequately airtight. I therefore removed the telephone and sealed all these parts with cement, thoroughly.

On replacing the telephone with the adjustment as in Fig. 6, the behavior had in fact changed, the negative pressure being of the small value indicated in §2, without growth in the lapse of time. In other words the presence of the pinhole c' within the closed region was now ineffective.

We may summarize these early results for the particular frequencies used, as in Figs. 9 and 10. In an air region R, closed on one side by a vibrating telephone plate T and on the other by a quiet plate U, the pressures are distributed as if there is a maximum at 7 and a minimum at U. If the region R, Fig. 9, communicates with the atmosphere by a pinhole 0 of the critical diameter, the pressure within R is raised as a whole by the amount which the pinhole air valve will withstand. Again if the closed region T U, Fig. 10, contains a pinhole valve O within only, it does not differ essentially from the corresponding case in Fig. 9; but if an additional very fine leak O' is supplied on the T side, Fig. 10, the U side gradually develops a large pressure decre

ment; whereas if the pinhole is supplied on the U side, this develops the usual pressure increment. In the former case air leaks out of O' diffusively; in the latter it leaks into O".

After many trials, however, only in one case did I succeed in obtaining pressure decrements with pinholes, screw cocks, etc.; this when lost could not be recaptured; but all the present and following results in acoustic dilatation were strikingly reproduced by putting a new telephone with unsealed plate in circuit.

With the apparatus, Fig. 1, and the cock C opened at the critical point, a diapason c" blown in the vicinity of the cock was easily identified and the octave c"" even three times as active (15 fringes). In another adjustment, the shrill overtone gave nearly 100 fringes. There is some misgiving in interpreting these data, as the open mouth of the pipe must usually be closed to the mouth of the cock; but as the overtone was still appreciably effective six inches to a foot away, the results are probably trustworthy.

8. Effect of Resonance.-While a parallel relation of the maximum pressure to the frequency of the telephone note has been shown to exist, it is obvious that the best conditions for high maxima will occur under conditions of resonance between the natural R and the T vibrations (Fig. 1) or their harmonics. I, therefore, used the same small induction coil with two storage cells, but with a commutator-like current-breaker, controlled by a small electric motor with a variable resistance in circuit (electric siren). By gradually decreasing this resistance all chromatic intervals between about f' and a" were obtainable. The speed of the motor, however, fluctuated slightly, while intervals within a semitone often produced large pressure differences. Thus the determinations of the intervals of a somewhat flickering pitch in all chromatics is quite difficult, even for a musical ear. A series of organ pipes within the given range seemed to offer the best standards of comparison, as it was necessary to turn rapidly from one series of observations to another.

In this way the graphs given in Figs. 7, 8, were worked out, the curves showing the fringe displacement s to the logarithmic frequency n of the telephone. In Fig. 7, to limit the deflections within the range of the ocular, about 2,000 ohms were put in circuit. Three maxima and three minima (one positive and two negative) are indicated. The maximum below f' could not be reached. The strong one at c" was well marked and approachable from both sides. The small one near g", though easily observed by continuously changing the pitch, was difficult to record.

The latter, however, is particularly interesting as it introduces the strong pressure decrements at a". I, therefore, reexamined it in Fig. 8 with less resistance (1,000 ohms) in circuit and the results came out more clearly. The deep minimum at a" deserves further investigation, as it precedes a probably very high maximum at the near c"". At least this may be inferred from the stimulation produced by an organ pipe used on the outside of the apparatus, §7. Something better than the electrical siren used will have to be devised; but apart from this the results are very definite.

Adjusting the siren for the maximum c", the sensitiveness with different resistances in circuit (2,000-9,000 ohms) was determined. The curve is shown in series 9, Fig. 3, and is the highest thus far obtained. The equation, rs constant, does not fit so well here, a result inseparable from the slightly fluctuating note; for this makes a big difference in the maximum. The mean value is about T8= = 80 X 103. Referred to a circuit resistance of 100 ohms this is equivalent to a deflection of 800 fringes and a pressure of Ap=.024 cm. of mercury.

An auxiliary telephone placed in circuit with that of T, Fig. 1, affords no suggestion of these occurrences. Its notes rather increase in strength regularly with the pitch. Yet if the note should happen to be near e", the other telephone would show no deflection.

Finally the use of the pin hole vent as a probe to detect the distribution of compression