938 MISCELLANEOUS GEOPHYSICAL METHODS [Chap. 12 



when quantitative reproductions of sound intensity and phase are required 

 (as in electrical direction-finding compensators). 



For detection purposes, receivers are generally arranged in groups either 

 along a horizontal base line, along a vertical line, on the surface of a 

 sphere, or on the circumference of a circle, all depending on the purpose of 

 the detection apparatus. For detecting low-frequency sounds (gun re- 

 ports, and the like) the hot-wire microphone (oi* "thermophone") is given 

 preference over the types just mentioned. It consists of a grid of platinum 

 wires of about 6 10" cm thickness, heated by an electrical current, and 

 placed in the neck of a Helmholtz resonator or in the passage between t^o 

 resonators. At these points the amplitude of the air moving to and fro is 

 greatest and produces variations in the temperature and therefore the 

 resistance of the platinum filament. When the microphone is arranged in 

 one of the arms of a Wheatstone bridge with an oscillograph in the de- 

 tector arm, it is possible to obtain a linear relation between oscillograph 

 amplitude and resistance variation and, therefore, the sound amplitude. 



The direction of sound is determined by the binaural effect, that is, the 

 ability to detect (subconsciously) very small differences in arrival time at 

 each ear. If the incoming sound makes the angle a with the connecting 

 (base) line of both ears and if d is their distance, the corresponding phase 

 shift is^"' 



A(p = — — cos a or At = - cos a (12-18) 



X V 



where X is wave length and v is velocity. 



In other words, the directional sensitivity of the ear depends on the 

 ratio d/\ (which also controls the directional properties of transmitters) 

 and amounts to about 3°, or a time difference of 30 microseconds. 



It is obvious that the directional accuracy can be increased by a binaural 

 device of larger base, as in airplane detectors. The direction of sound is 

 then determined by rotating the device until the base coincides with the 

 wave front. For airplane detection, two sets of "ears" (microphones in 

 parabolic reflectors or in horns) are required, one pair rota table about a 

 vertical axis to determine the horizontal azimuth, the other rotated about 

 a horizontal axis to obtain the vertical angle. 



If apparatus of this type is impracticable because of size, the phase 

 shift in the sound impulses received by a pair of detectors may be ascer- 

 tained by insertion of time-delaying arrangements. These may be me- 

 chanical (extension tubes) or electrical (compensators). Fig. 12-22 shows 

 a compensator employed in connection with a number of microphones 



1"^ This relation is identical with that relating time and apparent surface velocity 

 to emergence angle in seismology, see p. 541. 



