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 t 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.

20

-40

logn "d" ĕ" g′′ a

Since for sss the head is sλ/2 (the displacement being s fringes of wave-length λ), 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.

3. Resonator All but Closed.-If now the plug of the cock C is rotated from the open position gradually until the opening is reduced to the merest crevice, the fringe deflection s will, on further slow rotation, be

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, s, obtained. The maximum pressure obtained in these initial experiments was the equivalent of about 50 fringes; i.e., Ap=1.5 X 10-3 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, 8, when different resistances (given by the abscissas in 103 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 × 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 i=is. 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.,