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Unformatted text preview: Real pipes The pressure does not drop to zero right at the open end of a pipe. Because of this, the acoustic length is slightly grater then physical length. For a cylindrical pipe of radius r the end correction (additional length) is 0.61 r One open end: r L L acoustic 61 . + = Two open ends: r L r L L acoustic 22 . 1 61 . 2 + = + = For long pipes ( L>>r) the end correction can be neglected. For short pipes the end correction is important. One open end: r L L acoustic 61 . + = Two open ends: r L L acoustic 61 . 2 + = ... 5 , 3 , 1 44 . 2 4 4 44 . 2 4 4 1 1 = = + = = = = + = = n nf r L vn L vn v f n n r L n L acoustic n n acoustic n ... 3 , 2 , 1 44 . 2 2 2 44 . 2 2 2 1 1 = = + = = = = + = = n nf r L vn L vn v f n n r L n L acoustic n n acoustic n Principle of superposition and standing waves (optional) ) cos( ) , ( ) cos( ) , ( 2 1 t kx A t x y t kx A t x y + = = ( 29 ( 29 ) sin( ) sin( ) sin( ) sin( 2 ) , ( t kx A t kx A t x y sw = = ) cos( ) cos(...
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This document was uploaded on 02/11/2012.
 Fall '09
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