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EAMCET Engineering 2010 Solved Paper
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© examsnet.com
Question : 91
Total: 160
An organ pipe
P
1
, closed at one end and containing a gas of density
ρ
1
is vibrating in its first harmonic. Another organ pipe
P
2
, open at both ends and containing a gas of density
ρ
2
is vibrating in its third harmonic. Both the pipes are in resonance with a given tuning fork. If the compressibility of gases is equal in both pipes, the ratio of the lengths of
P
1
and
P
2
is (assume the given gases to be monoatomic)
1
3
3
1
6
√
ρ
1
ρ
2
1
6
√
ρ
2
ρ
1
Validate
Solution:
Frequency of closed organ pipe for first harmonic
n
1
=
v
1
4
l
1
.
Frequency of open organ pipe for third harmonic
n
3
=
3
v
2
2
l
2
At resonance,
n
1
=
n
3
or
v
1
4
l
1
=
3
v
2
2
l
2
or
l
1
l
2
=
1
6
(
v
1
v
2
)
l
1
l
2
=
1
6
√
B
ρ
1
×
√
ρ
2
B
=
1
6
√
ρ
2
ρ
1
© examsnet.com
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