A SELECTIVE HOT-WIRE MICROPHONE. 
399 
The forced vibrations of a resonator, due to an external source of sound, have been 
considered by Rayleigh (“ Theory of Sound,” vol. IT., p. 195). If the periodic change 
of pressure at the mouth of the resonator is represented by ¥e' pt , the equation of 
motion applicable to the forced vibration in the neck is 
d 2 x 
d¥ 
p 2 c dx , o 
+n‘ 1 x - 
2ttY dt 
cF 
P 
e lpt 
where c is the hydrodynamical conductivity of the neck and p is the density of the air. 
Idle term representing dissipation is here a function of frequency, but it represents “ only 
the escape of energy from the vessel and its neighbourhood, and its diffusion in the 
surrounding medium, and not the transformation of ordinary energy into heat.” It 
is found to be quite inadequate to account for the experimentally determined rate of 
dissipation. If p/ 2tt = 112 vibrations per second, c = 0T3 cm. (determined experi¬ 
mentally), and V = 33760 cm. per second, then 
p 2 c 
4ttV 
0-15, 
which must be compared with the experimentally determined value of 22 -2. It is clear, 
therefore, in the case of resonators such as those used in these experiments, that the 
dissipation is due in the main to other causes than the escape of energy through the 
neck, such as the effect of viscosity on the motion in the neck, and the lack of rigidity 
in the walls of the container. When we consider the obstructions caused by the glass- 
enamel rod supporting the grid and the sharp edge of mica at the base of the neck, 
the comparatively high rate of dissipation is not altogether surprising. 
The expression for the natural frequency of a Helmholtz resonator (calculated without 
allowance for dissipation) is 
If N is found from the resonance curve and S is measured, the conductivity c can be 
calculated, and this should be a constant for a given size and shape of neck. For the 
cylindrical necks 2 -2 cms. long and 0 -75 cm. in diameter, and partially obstructed by 
the platinum wire grid, it is found that c is about 0 T3 cm. The following is an example 
of the kind of measurement taken :■—- 
N. 
vibrations/sec. 
S. 
c.c. 
c 
cm. 
240 
68 
0-133 
235 
73-6 
0-138 
140 
197 
0-131 
116 
290 
0-132 
Temperature 13 
• 3 C. Mean value of c 
= O' 133 cm. 
3 i 2 
