98 



ACOUSTICAL ELEMENTS 



in problems in acoustics involving the use of tubes. The equation ^^ ex- 

 pressing the sound transmission in a tube is 



A = A,e-"- 5.58 



where A = amplitude (pressure or volume current) at a distance x cen- 

 timeters from the amplitude ^o, 



RcSlp 

 R = radius of the tube, in centimeters, 

 c = velocity of sound, in centimeters per second, 

 OJ = 2x/, 



/ = frequency, in cycles per second, 

 M = viscosity coefficient, L86 X 10"^ for air, 

 p = density, in grams per cubic centimeters, 

 7' = 1 + L58(y/2 _ ^-1/2)^ and 

 7 = ratio of specific heats, L4 for air. 

 The attenuation characteristics of tubes of various diameters as a func- 

 tion of the frequency is shown in Fig. 5.9. 



FREQUENCY IN CYCLES PER SECOND 



Fig. 5.9. The attenuation of a sound wave in decibels per foot as a function of the frequency 

 in cycles per second in pipes of various diameters and filled with dry air at 20° C. 



5.25. Transmission of Sound from one Medium to Another Medium. 



— It is the purpose of this section to consider the transmission of sound 

 energy across a junction of two media. The boundary between the two 

 30 Mason, W. P., Phys. Rev., Vol. 31, No. 2, p. 283, 1928. 



