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JEE Main 16 March 2021 Shift 2 Solved Paper
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© examsnet.com
Question : 28
Total: 90
A closed organ pipe of length
L
and an open organ pipe contain gases of densities
ρ
1
and
ρ
2
respectively. The compressibility of gases are equal in both the pipes. Both the pipes are vibrating in their first overtone with same frequency. The length of the open pipe is
x
3
L
√
ρ
1
ρ
2
where
x
is ......
(Round off to the nearest integer)
[16 Mar 2021 Shift 2]
Your Answer:
Validate
Solution:
First overtone of open pipe
=
V
2
L
2
First overtone of closed pipe at one end
=
3
v
4
L
As per question,
3
V
4
L
=
V
2
L
⇒
√
B
ρ
1
⋅
3
4
L
=
√
B
ρ
2
⋅
1
L
2
(
∵
V
=
√
B
ρ
)
⇒
L
2
=
4
L
3
√
ρ
1
ρ
2
....(i)
According to question, the length of the open pipe is
x
3
L
√
ρ
1
ρ
2
....(ii)
Comparing Eqs. (i) and (ii), we get
x
=
4
© examsnet.com
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