100 ACOUSTICAL ELEMENTS 



The ratio of the transmitted power to the incident power is from 

 equations 5.59, 5.60, 5.61, 5.62, 5.63 and 5.64. 



Pn = , '"f " ,, 5.65 



The above formula may be used to compute the acoustic resistance of 

 materials from the absorption coefficient for materials which do not exhibit 

 a reactive component. 



The above formulas are also applicable to the sound transmitted across 

 the junction of two semi-infinite pipes having acoustic impedances vax 

 and Taz- 



5.26. Tubes Lined with Absorbing Material. — In ventilator and ex- 

 haust systems it is desirable to provide a high degree of attenuation for 

 audio frequency waves while offering low resistance to continuous flow. 

 For that purpose one of the most satisfactory systems are ducts lined with 

 absorbing material. Longitudinal isolation of the walls of the duct should 

 be provided to prevent longitudinal transmission of sound by the walls of 

 the duct. This can be accomplished by the use of rubber connectors at 

 regular intervals. The walls of the duct should be rigid so that air borne 

 sounds are not transmitted through the walls. Very high attenuation 

 can be obtained in ducts of this type. For example, a circular duct 12 

 inches in diameter lined with 1-inch rockwool gives 2 db attenuation per 

 foot over the frequency range from 80 to 250 cycles. Above 250 the at- 

 tenuation rises rapidly, being 6 db per foot at 500 cycles and 20 db per foot 

 at 1000 cycles. The effect of d.c. air flow up to 2000 feet per minute does 

 not appreciably change the a.c. attenuation. The general subject ^^ of 

 tubes lined with absorbing material, with both rigid and vibratile walls, 

 has been considered theoretically and experimentally. 



Sivian, L. J., Jour. Aeons. Soc. Amer., Vol. 9, No. 2, p. 135, 1937. 



