The Effects of Viscosity And Heat Conductivity On the Transmission of Plane Soun

Cover The Effects of Viscosity And Heat Conductivity On the Transmission of Plane Soun
The Effects of Viscosity And Heat Conductivity On the Transmission of Plane Soun
John R Knudsen
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Rf i X-C t| X 'I "\ C tf> O 1 c 2 T \ In a small k Interval c:;ntered about k = we consider 6u for large fixed t. Pig. 3 shows Su for various values of T . For decreasina; values of T. The curves become steeper Fig. 3 approaching the square wave limit situation. For indefinitely largo t the velocity 5u becomes 9.
1- erf /^^ v/hlch in any k Interval depends on T^ . Thus more information is obtained by our present observer than by the earlier one for which the ultimate value of 5u turned out to b
...e sj. Mply p* over any snail x -Interval.
In the event that after a relatively small finite time t, the velocity at x = is suddenly reduced to zero a second wave front is propagated to the right in the channel. It moves into the wake of the first wave front causing it to decay or die out. From the better vlevjpoint of the observer X = kc /t"+ c t we obtain for Su the asymptotic expansion ( 2 . 06 ) 5u /27iT. T A I, ' kt.
2T /2^ y(y+3T J7t 1 - e Yt.
\ -T7^(Jt + k)2 ^■\ 1 - erf k x - c t or, with k = (2.


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