46 



BELL SYSTEM TECHNICAL JOURNAL 



the force factor and impedance of the recei\-hig circuit. Modification 

 of any of these may produce marked changes in the resulting howling. 



The way the length / enters the formula (54) for sustained howling 

 indicates that the curves representing the possible frequencies of 

 howling, that is, frequencies which produce equality of phase on both 

 sides of the equation, vary periodically with the length. 



The intersection of the branches of these curves on any given 



frequency line will be separated by distances corresponding to -, 



that is, corresponding to a wave length at the pitch corresponding 

 to /. Also, if the supply current is reversed, that is, the sign of I 



TUBE LENGTH 

 3fo5CMS 



Fig. 10 



changed, and the length of the tube varied until the frequency of 

 howling is brought back to the original value, the change in length 



must be equal to — • For since the frequency is unchanged all the 

 2/ 



quantities in equation (54) remain unchanged except the sine and 

 cosine factors. Adding a half wave length Is equivalent to adding x 

 to the angle which makes the left hand member the negative of its 

 first value, and consequently, restores the phase equality. 



Using the circuit shown in Fig. 10 for the electrical coupling, the 

 frequency of howling was computed for \arious tube lengths, the 

 results being given in Fig. 11. 



The instrument constants were those used before, the other values 

 being Vr = 1.^ cc, Fr = 6.4 cc, and q = .^7 cm.^, a = 3.43Xl04 cm/sec. 

 p = . 001203 gm/cm^. Using these values the formulae for N and P 

 become 



,V=(_1.31/5 + 7.5/3-9.G8/+3.26^)Xl0^+j(-141/'- 



.63/2 + .36)Xl08, 



p = (5.5/^- 12.35/2 + 6.77) X10s+i( -.60/3 + . 66/) X10^ 



where / is the frequency in kilocycles. 



The points on the calculated curves of Fig. 11 were obtained by 

 direct experimental observation with the circuit shown, and with 

 various lengths of brass tube coupling the transmitter and receiver 

 together. The agreement between the calculated and observed 



