A SELECTIVE HOT-WIRE MICROPHONE. 
405 
the form of heat is lost mainly by convection. There is in fact above the grid a free 
convection current whose velocity depends on the temperature and diameter of the 
platinum wire. A sound of suitable pitch produces in the neck of the resonator an 
alternating current of air which is superimposed upon the free convection current, 
with the result that the convection of heat from the platinum wire is alternately retarded 
and accelerated. It can easily be seen that if the maximum velocity of the alternating 
air-current does not exceed the velocity of the convection current, the periodic tempera¬ 
ture change produced in the platinum wire will have the same frequency as that of the 
sound stimulating the resonator. 
This is in accordance with the observed fact that when the microphone is held 
vertically the note heard in the telephones has the same pitch as that of the original 
sound. 
Next, suppose that the microphone is held so that its axis is horizontal and the grid 
lies in a vertical plane. The free convection current is now at right angles to the axis 
of the neck, and the effect of an oscillatory motion of the air in the neck (parallel to its 
axis) will be to produce a periodic change in the temperature (and therefore resistance) 
of the grid whose periodicity will be twice that of the sound which produces it. This 
is in fair agreement with observations, for when the microphone is gradually tilted 
over from a vertical to a horizontal position, the fundamental note heard in the telephone 
slowly dies away and the octave becomes more and more prominent. The octave is 
heard best, however, when the neck is pointed slightly downwards so that the axis 
makes an angle of about 20 degrees with the horizontal. This peculiar effect, which 
appears to be due to the asymmetrical construction of the neck of the resonator, will be 
referred to in a later paragraph (§8). 
We shall in the present section confine our attention to the case when the microphone 
is held vertically with the neck pointing upwards, and it will be assumed that the 
resistance changes which the sound produces in the grid can be attributed to the changes 
in the velocity of the air in the neck. In order to ascertain the nature of the resistance 
changes which are likely to occur, it is first of all necessary to determine the relation 
between the resistance R of the grid and the velocity U of the air-current which cools 
it. U here refers to the velocity of the forced air-current, the actual current passing 
the wires of the grid being the sum of the forced current and the free convection current. 
The velocity of the undisturbed convection current rising from the grid will not, of course, 
be evenly distributed in the neck of the resonator, but the effects of free convection can 
be represented by an “ effective ” current V 0 supposed uniform throughout the neck. 
The actual current passing the grid is then V = U + V 0 , the downward vertical being 
regarded as the positive direction. We shall first obtain a relation between R and U 
for small steady values of U, and afterwards extend the results obtained to the case of 
oscillatory currents by putting U sin pt in place of U. 
On account of the applications to be found in Hot-Wire Anemometry, the cooling of 
electrically heated fine platinum wires by steady currents of air has received a good deal 
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VOL. CC'XXI.-A 
