458 Appreciation of Difference of Phase of Sound- Waves. % 



a maximum change in direction before the phase-difference 

 of a wave-length was readied for the fork of shorter wave- 

 length, but did not find such a maximum for the graver 

 tone. And also we should remember that in the problem of 

 locating sounds of these pitches in the free air, such large 

 differences of phase would not occur. For example, the 

 average distance between the ears of a man is about 15*5 

 centimetres, and that is less than a quarter of these wave- 

 lengths. 



If it be granted that we locate sounds entirely by their 

 phase relations up to a phase-difference determined by the 

 distance between the ears, we still find this insufficient as an 

 explanation for locating sounds which come from the extreme 

 right or left. For these large, angles, difference in intensity 

 may be our principal aid, especially as the head is best fitted 

 then to cast a sound shadow. It is also a matter of observa- 

 tion that it is not so easy to locate either very grave tones or 

 very shrill ones, and this may possibly be so because the 

 difference in path to produce a phase-difference of a quarter 

 of a wave-length is either much greater or much less than 

 the width of the head. 



During the experiments, attention was paid to the question 

 whether difference in phase produced a change in the in- 

 tensity of the combined tones. Analytically two sounds 

 interfere when the phase-difference is a half wave-length. 

 But the mind evidently does not combine the separate sensa- 

 tions in the ears in so simple a manner, as not one of the 

 observers could detect any alteration in the loudness of the 

 sounds when the relative phases were changed. Neither 

 were they heard as two tones, nor was the sound louder in 

 one ear than in the other. The effect was as if the fork had 

 been sounded in the free air at different points on the cir- 

 cumference of a circle. 



These experiments are perhaps open to the objection that, 

 to produce a difference in phase, one branch tube must be 

 made longer than the other. And so a doubt may arise 

 whether the intensity of the sound going through the longer 

 tube is not diminished more than that through the other 

 tube. But the observations show that this objection is not 

 valid. If it were a question of change of intensity, the change 

 in direction would increase continually and not reach an 

 angle where further increase in length of the tube produces 

 either a doubtful increase in angle or even at times a decrease. 

 We tested the least change in the relative lengths of the 

 tubes which would shift the angle appreciably and found, 

 for some listeners, two centimetres to be sufficient. The 



