next up previous
Next: References Up: Review of related mathematics Previous: Examples:

(b) ``Small'' disturbance approximations

figure255

Q: How can tex2html_wrap_inline637 and tex2html_wrap_inline639 be approximated for ``small'' values of tex2html_wrap_inline617 , tex2html_wrap_inline619 compared to x?

(b1)

eqnarray261

where    tex2html_wrap_inline645

eqnarray276

For tex2html_wrap_inline647 tex2html_wrap_inline649

For also small tex2html_wrap_inline651 , then:

eqnarray284

Example: tex2html_wrap_inline653

eqnarray288

Exact     tex2html_wrap_inline655

For : tex2html_wrap_inline657

eqnarray297

Exact     tex2html_wrap_inline659

(b2) Approximation of ``l''

eqnarray302

So for tex2html_wrap_inline661  then

the terms tex2html_wrap_inline663  are smaller than 1 and tex2html_wrap_inline665

For example : tex2html_wrap_inline667

eqnarray324

So finally   tex2html_wrap_inline669  for tex2html_wrap_inline671

Example: tex2html_wrap_inline673

Exact    l=1.1045


Soon Woong Chang
Wed Sep 29 15:22:46 CDT 1999