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Full text of "Scientific Papers - Vi"

382     PROPAGATION OF SOUND IN NARROW TUBES OF VARIABLE SECTION   [402
As an example let us take the case of a tube of revolution for which y, being equal to y0 over the regular part, becomes y0 + Sy between x1 and xs. We have
Also*
1    _     1    Jdx
^-
J 1/o                  2/0
V    o-R    ,         .     Pafrt/'s^2                     7
and                5-+-o-=(*s-a'i)+      ]2    +jh;      rrfa?> ......... (38)
2cr      2                     J*, I   V^/o/      4 \diK ) }                   ^    '
the terms of the first order in 8y disappearing.    Thus in the exponent of (35)
. . .(39)
of which the right-hand member, taken with the positive sign, expresses the retardation of the transmitted wave due to the departure from regularity.
* Theory of Sound,  308.sufficient approximation.    Thus