Tortuosity ensures that the sound waves in a porous material do not travel in a straight path but interact with the pores in a tortuous path thus having maximum energy transfer at the pores. The tortuosity (aj is determined by using the empirical formula in terms of porosity (H) as given by Eq. (10)35.

6.5.3.2 CHARACTERISTIC LENGTHS

There are two measures of characteristic length which are of use. The viscous char­acteristic length is related to the size of the interconnection between two pores of the porous sound absorbing material. The thermal characteristic length is related to the diameter of the pore of the interconnecting channels. The thermal characteristic length is given as the ratio of the total inner surface area to the volume of the pore.

Here, the viscous and thermal characteristic lengths were estimated based on Allard’s model and its extensions to Biot theory35. Assumption was made that jute fibers are cylindrical. Viscous characteristic length (л) depending on the frame ge­ometry and is given by Eq. (11)

1

л =———-

2nrl

where 2nrl is total perimeter of fiber per unit volume of material, is diameter of fiber and total length of fiber per unit volume of material defined by Eq. 12

l =-£- (12)

nr p

p and p’ are density of the sample and density of fiber, respectively.

Allard showed that for the material with porosity close to unity, л’ = 2 л. For

material having pores of triangular cross section, л’= 1.14 л where л’ is thermal characteristic length35.

The above properties of these jute felt and jute fibers are shown in Table 6.8. The range of diameter of jute fibers which was measured by scanning electron mi­croscope is 50-90 pm. By the statistical averaging of diameter at different locations, the effective diameter of single jute fiber is 68 pm. Density is about 1084.4 kg/m3.