Page 1 Sound Propagation through Media Nachiketa Tiwari Indian Institute of Technology Kanpur Page 2 Sound Propagation through Media Nachiketa Tiwari Indian Institute of Technology Kanpur LECTURE-31 1-D Waves In Tubes Page 3 Sound Propagation through Media Nachiketa Tiwari Indian Institute of Technology Kanpur LECTURE-31 1-D Waves In Tubes Impedance In 1-D Tubes Table 31.1 Characteristic Specific Tube Impedance Acoustic Impedance Infinitely Long Tube Z 0 = ? 0 c Z 0 = ? 0 c Finite Tube With Closed End Z 0 jZ 0 .cot( ?x/c) Finite Tube With Open End Z 0 -jZ 0 .tan( ?x/c) Page 4 Sound Propagation through Media Nachiketa Tiwari Indian Institute of Technology Kanpur LECTURE-31 1-D Waves In Tubes Impedance In 1-D Tubes Table 31.1 Characteristic Specific Tube Impedance Acoustic Impedance Infinitely Long Tube Z 0 = ? 0 c Z 0 = ? 0 c Finite Tube With Closed End Z 0 jZ 0 .cot( ?x/c) Finite Tube With Open End Z 0 -jZ 0 .tan( ?x/c) 1-D Waves In Short Tubes • Table 31.1 provides functions for specific acoustic impedance I(x , s) for different types of tubes. We consider each of these tubes in a case-by-case basis. • For an infinitely long tube, P + /V + is a constant and equals Z 0 . Thus: • Next we consider an open tube. For such a tube: Eq. 31.1 Page 5 Sound Propagation through Media Nachiketa Tiwari Indian Institute of Technology Kanpur LECTURE-31 1-D Waves In Tubes Impedance In 1-D Tubes Table 31.1 Characteristic Specific Tube Impedance Acoustic Impedance Infinitely Long Tube Z 0 = ? 0 c Z 0 = ? 0 c Finite Tube With Closed End Z 0 jZ 0 .cot( ?x/c) Finite Tube With Open End Z 0 -jZ 0 .tan( ?x/c) 1-D Waves In Short Tubes • Table 31.1 provides functions for specific acoustic impedance I(x , s) for different types of tubes. We consider each of these tubes in a case-by-case basis. • For an infinitely long tube, P + /V + is a constant and equals Z 0 . Thus: • Next we consider an open tube. For such a tube: Eq. 31.1 1-D Waves In Short Tubes • if the tube were “short ” i.e. Or , then: • Also, Eq. 31.2 • Similarly for short closed tube (i.e. when l<< ?/2 p): Eq. 31.3Read More

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