Inductance method

The inductance method due to Kergomard and Garcia [57] is reviewed
here. The multimodal method was treated and the results used
to get a polynomial for the frequency dependent inductance, ,
so that the formula

Now we will work out the reflectance for a plane wave incident on a discontinuity between two infinite cylinders. We do this by expressing both the equations in (C.1) in terms of forward and backward going waves and solving. The pressure on the left is the sum of incident and reflected waves: . The pressure on the right is simply the transmitted term .

The volume velocity on the left is then

(C.2) |

(C.3) |

Now we turn to the first part of equation (C.1). Substituting in the pressure as the sum of the forward and backward going waves and putting gives

In order to work out the reflectance we need to remove to obtain an expression featuring only and . We therefore substitute from equation () into equation (C.5).

(C.6) |

As with the multimodal method this may be expressed in terms of dimensionless variables and ;

where is a function of the dimensionless variables and is tabulated in table 2 (A) of [57]. This formula is used to calculate the inductance method reflectance shown in figure 6.1 of section 6.4.

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