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lecture07

# lecture07 - Real pipes The pressure does not drop to zero...

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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 . 0 + = Two open ends: r L r L L acoustic 22 . 1 61 . 0 2 + = + = For long pipes ( L>>r) the end correction can be neglected. For short pipes the end correction is important.

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One open end: r L L acoustic 61 . 0 + = Two open ends: r L L acoustic 61 . 0 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 λ λ λ ... 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 λ λ λ
Principle of superposition and standing waves (optional) ) cos( ) , ( ) cos( ) , ( 2 1 t kx A t x y t kx A t x y ϖ ϖ + - = - = ( 29 ( 29 ) sin( ) sin( ) sin( ) sin( 2 ) , ( t kx A t kx A t x y sw ϖ ϖ = = ) cos( ) cos( ) , ( ) , ( ) , ( 2 1 t kx A t kx A t x y t x y t x y ϖ ϖ + - - = + = A A sw 2 = - + = - 2 sin 2 sin 2 ) cos( ) cos( α β β α β α

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Helmholtz resonator Singing rods
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lecture07 - Real pipes The pressure does not drop to zero...

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