JEE Physics/ Lakshmikanta Satapathy/ Wave Motion QA part 3/ JEE question on fundamental frequencies of Open and Closed pipes solved with the related concepts

1. Physics Helpline
L K Satapathy
Wave Motion 3
Harmonics in Open and Closed Pipes
L L

2. Physics Helpline
L K Satapathy
Wave Motion 3
Question : A pipe open at both ends has a fundamental frequency f in air. The pipe
is dipped vertically in water so that half of it is in water. The fundamental frequency
of the air column is now
Concepts :
3
( ) ( ) ( ) 2 ( )
2 4
f f
a b c f d f
L
(i) Open Pipe :
In case of an open pipe , anti-nodes are formed at both ends
 In fundamental mode , there is 1 node between the two
If wave length =  and length of pipe = L , then
2 ... (1)
2
L L

  

/2 /4

3. Physics Helpline
L K Satapathy
Wave Motion 3
L
(ii) Closed Pipe :
In case of a closed pipe , there is an anti-node at one end
and a node at the other
If wave length =  and length of pipe = L , then
4 . . . (3)
4
L L

  
If speed of sound = v , then fundamental frequency is given by
. . . (4)
4
o
v v
f
L
 
 In fundamental mode , there is NO node between the two
If speed of sound = v , then fundamental frequency is given by
. . . (2)
2
o
v v
f
L
 

4. Physics Helpline
L K Satapathy
Wave Motion 3
Correct option = (d)
[ ]' sf f An 
. . . (5)
2
v
f
L
 
Answer :
L
In the Q , let the length of the given open pipe = L
Given that fundamental frequency = f
 Equation (2)
L /2
When half the length is in water , it becomes a closed tube
Let its fundamental frequency 'f
' . . . (6)
4 ' 2
v v
f
L L
   Equation (4)
whose effective length
2
L
L 

5. Physics Helpline
L K Satapathy
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