COLLECTION OF SOUND 



303 



wave form. Physically the distortion is due to the nonlinearity of the 

 atmosphere. The harmonics generated in an exponential horn have been 

 considered in Sec. ^.oA. The distortion generated in a sound wave propa- 

 gated in air is of interest in certain problems involving high sound levels. 

 The ratio of the second harmonic, generated in a plane sound wave, in 

 traversing a distance x, to the fundamental is 





(7 + \)lTrp,fx 



12.13 



where 7 = ratio of specific heats, 1.4 for air, 



px = fundamental sound pressure, in dynes per square centimeter, 

 pQ = atmospheric pressure, in dynes per square centimeter, 

 pi = second harmonic sound pressure, in dynes per square centi- 

 meter, 

 c = velocity of sound, in centimeters per second, 

 / = frequency, in cycles per second, and 

 X = distance, in centimeters. 

 The distance which a plane wave must travel to produce 1 per cent 

 distortion for a pressure of 1, 10 and 100 dynes, for frequencies of 100, 1000 

 and 10,000 cycles, is shown below. 



12.3. Collection of Sound. — A. Sound Collecting System 25.25-4. — When 

 a source of sound is caused to act in a room, the first sound that strikes a 

 collecting system placed in the room is the sound that comes directly from 

 the source without reflection from the boundaries. Following that comes 

 sound that has been reflected once, twice and so on, meaning that the 

 energy density of the sound increases with the time, as the number of 

 reflections increase. Ultimately, the absorption of energy by the bound- 

 aries equals the output of the source and the energy density at the col- 



25 Olson, H. F., Proc. Inst. Rad. Eng., Vol. 21, No. 5, p. 655, 1933. 

 25^ Olson and Massa, "Applied Acoustics," P. Blakiston's Son and Co., Philadel- 

 phia. 



