250 DR. LOUIS VESSOT KING ON THE PROPAGATION OF SOUND IN THE FREE 
suspected that these were in some way connected with the free periods of vibration of the mica diaphragm 
(loaded at the centre) the resonator chamber and back of the phonometer were entirely removed. It 
was then found that resonance occurred at the following frequencies : 
297, 381, 582, 1141, 2060. 
Numbers differing but slightly from these or their sub-multiples could be recognized among the resonance 
frequencies observed with the resonator in position.* Any note having among its harmonies one of the 
free periods of the mica diaphragm would show resonance. As the frequencies of these spurious resonances 
were far removed from that of the diaphone note when sounded over the normal range of air-pressures, the 
matter was left aside as of subsidiary importance to the main work on hand. In the following table are 
given the final results of the determinations of resonance frequencies corresponding to the various resonator 
positions (denoted by h and expressed in centimetres). 
Table I. 
Resonator 
position. 
h (cm.). 
Frequency. 
n. 
n? x (Ji + 10 *8 cm.). 
Resonator 
position. 
h (cm.). 
Frequency. 
71 . 
n- x ([h + 10 "8 cm.). 
o-o 
232 
5-72 x10 5 
6-0 
185-5 
5-78 X 10 5 
1-0 
224 
5-93 
7-0 
177 
5-67 
2-0 
217-5 
6-04 
8-0 
174-8 
5-72 
3-0 
206 
5'85 
9-0 
168-5 
5-62 
4-0 
200 
5-92 
10-0 
166 
5-75 
5-0 
193 
5-88 
Mean . . . 
5-81x10 5 
According to the elementary theory, the resonance frequency of a resonator of volume Q is given by 
the formula! 
n = (c/2ir) J{ K/Q),.(v.) 
c being the velocity of sound at the temperature of the experiment given by 
c = Co(l 1--| cd ) = (33130 + 61/) cm./sec., . .(vi.) 
where a. — 0 - 00367 and t is the temperature in degrees C. 
K is the “ inertia coefficient” or “ conductivity” of the aperture; for a circular aperture of radius R in 
an infinitely extended thin wall K = 2R. 
We may write Q = d 2 (]i + ho), where d is the diameter of the resonator and h 0 is the mean length of 
the cylindrical chamber at position 0. 
Ey taking h 0 = 10 "8 cm., we notice from Table I. that the product n 2 (h + ho) is constant within the 
limits of observational errors, as required by theory. Formula (v.) may then be written 
m, 2 (A+10’8) = -~ s Kc q /d 2 = 5 * SI x 10 5 .(vii.) 
Taking c = 3 - 40xl0 4 cm./sec. at t — 15° C., d= 11 7 cm., we derive for Iv in (vii.) the value 
K = 2 - 12 cm. The diameter of the aperture of the phonometer resonator was 2R = 2-50 cm. 
The exact theoretical calculation of K for the aperture of a resonator of the type under consideration 
has not yet been carried out as far as the writer is aware; the above experimental determination shows 
* The resonance frequencies of free edge-clamped diaphragms have been carefully studied by Hilleb, D. C., ‘The 
Science of Musical Sounds,’ Macmillan and Co., New York, 1916, pp. 148, et seq. 
t Ratleigh, 1 Sound ’ (1896), vol. ii., p. 304. 
