The Acoustic Pressure in Tubes Capped by High Resistance Telephones, Vibrating in Different Phases

VOL. 11, 1925

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THE ACOUSTIC PRESSURE IN TUBES CAPPED BY HIGH RESISTANCE TELEPHONES, VIBRATING IN DIFFERENT PHASES* By CARL BARus D1PARTmsNT O PHYSICS, BROWN UNIVI8RSIrY Communicated August 1, 1925 1. Apparatus.-As in the preceding papers (these PROCUUDINGS, May, July), the acoustic pressure is measured by pin hole probes at the middle of the tube connecting the telephones, communicating with the interferometer U-tube The fringe displacement is s. In dealing with larger inductances the radio telephones are clearly more useful. Furthermore an enlargement of the end connections of the pipe joining the paired telephones suggested itself. Hitherto the junction had been made with perforated rubber stoppers and quill tubes connectors. In the present case the tube ends were attached to the telephone mouth pieces directly, in order to introduce the least obstruction possible. The result, however, was but a slight rise in pitch from the former a', to 'b' in the present adjustment. Figure 1 gives evidence of the extreme sharpness of the resonance crests for the summational position of the switch S (phase). Below c', however, there is multiresonance which is difficult to construe, as a definite 'b' crest could not be found unless the diffuse c' crest here replaces it. The occurrence of the sharp strong 1b" crest must have had an analogue in the preceding work, though for some reason it was not detected. It may have been deadened by the quill tube connectors. The sequence curve is very weak throughout and practically without elevation at Lb' and LY. It has, however, picked up its own small harmonics at f' and M" with a little one near b. It is interesting to inquire into the cause of the crests in the sequence graphs, figure 1 or 2. Since the f is the fifth of 'b and the telephone note is rich in overtones, one may surmise that in the sequence graph, while the bb is eliminated, thef overtone would not be. In fact if we take the usual equations y = a sin (so-soo) and y' = a' sin ((p + poo'), the compound harmonic is A sin (so-l0), where tan ,o = Za sin (oo/Za cos oo and Aa = (2a sin 'po)2 + 2(a cos (po)2. Hence if we put a = a', (po = 0 and soo' = ir/2 for the f harmonic, it follows that -o = 450 and A = a
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present adjustment to meet the case of large resistances and inductances, the small inductor I, figure 2 (about 0.35 henry in each secondary I', I), was inserted as there shown, using the commutating device C for the exchange of auxiliary inductances L, L', etc. Each telephone, T, T', has its own secondary and T' is provided with a switch S. B is the (motor) periodic break. Under these circumstances a single cell at E will throw the crests of the phase graph far out of the field of view. The sequence graph, figure 2, is correspondingly developed with thef crests sharper than in figure 1. The strong b crest, here obtained, is a new feature and there was a further marked development even as low as c. These crests, however, are to be avoided and the measurements made corresponding to the sharp 'b" or 'b' resonance in the phase graph.

4-

60

4i

140 dca, ac& f e" ef a,

100

100

8~~~~0

2-

3

r JO102

04

There are two difficulties encountered in making these experiments: The first is the sharpness of the resonance crests, the other the rather slow growth of the maximum displacement. Examples of typical results are given in figures 3 and 4, which are sequence graphs obtained by the method figure 2. The group a refers to a comparison of external resistances (R = 0, R' = 0 to 4 X 104 ohms) only; the graph b, to a comparison of L1 + L4 (0.36 heiRry and 10 ohms) with R (0 to 4 X 104) and the graph c to L3 (1.4 henry and 550 ohms) with R. To these must be added the internal resistances Ro and inductances Lo of the telephones and coils T, I and T', I', respectively. The

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discussion of the curves is complicated by the unequal efficiency of the telephones considered in the last paper, and by the unequal induction E, E' of the two coils. As a result the upper curves of a pair are usually without well developed minima; whereas the lower curves (commutated) often show pronounced minima, on the two sides of which the sound passes apparently from one telephone to the other. This minimum will be determined by the superposition of an R-graph decreasing with R and an L-graph increasing with R. If we place the minimum at their intersection, s' = s cancels out and for currents i = s/c, etc., the equation for parallel coupling reduces to, c2 { (R + RO)2 + Lo W2} = c R2 {Ro + (L + Lo)2w2 } and gives a good order of values for the minimum at R if the load is L. One notes that the R position of the minima as well as the intersection of the paired graphs rise with increasing L. 3. The Intersection of Paired Graphs.-If we treat the present experiments in which the currents in the T, T' circuits are coupled by mutual induction as if they were ordinary currents in parallel, the results are a close approach to the actual case. The later data of figures 3 and 4 are available for testing the case by computing R for the points I at which the graphs b and c intersect. The equation for the purpose has been given (As = As') heretofore and may be put in the form

c'/V(R' + R )2 + L'ow2 + c/V(R + Ro)2 + Low2 = c'//(Ro + RX)2 + (Lx + L')2w2 + c/N/(Ro + RX)2 + (Lx + Lo)2W2 Here Rx and Lx are the resistance and inductance of the coil commutated and R' = R is the observed resistance at the point of intersection. Ro, Lo, R', L are the constants of the secondaries and telephones as indicated in figure 1. The data are, since co = 2934, L = 1.2 Telephones: T', Ro' = 1110, Lo' = 1.2 T, Ro = 1090 Secondaries:

I',

30

0.4

I,

32

0.3

Total:

Total Ro = 1122 Lo = 1.5 Ro' = 1140, Lo' = 1.6 These.values are nearly enough alike for the T and T' circuits that a mean may be taken tentatively, with the object of simplifying the cumbersome equation just stated. This reduces, if L = L', R = R' and R = R' at the intersection to

(R + R0)2 = (Rx + R0)2 + t(Lx + Lo)20L2}w2. If now Rx, Lx refer to the coils L, + L4 of the graph b, figure 4, Rx = 11 and Lx = 0.36, from which R = 2380 ohms. The point of intersection in figure 4, b is at about 2000 ohms. If Rx, Lx refer to the coil L3 of graph c, figure 3, Rx = 550 ohms, L3 = 1.4 henry, from which R = 6511 ohms, while the point of intersection in figure 3 c is between 4000 and 5000 ohms.

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In both cases therefore the computed point of intersection lies above the point given by the graphs; but the order of values is satisfactory, as one cannot expect sharp values from the approximate current equations i = s/c and i' = s'/c', nor the coupling postulated. Moreover the same equations have been made to include the inequalities of induction E, E'. The equation for (R + Ro)2, shows that the point of intersection of the paired curves moves to the right both with Rx and Lx of the commutated coils. * Advanced note from a Report to the Carnegie Institution of Washington, D. C.