Sound Propagation through Media 1-D Waves In Tubes Notes | EduRev

: Sound Propagation through Media 1-D Waves In Tubes Notes | EduRev

 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. 31.3 
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