wave_mechanics organ_pipe_vibration_of_air_column Question 51
Question: An organ pipe open at one end is vibrating in first overtone and is in resonance with another pipe open at both ends and vibrating in third harmonic. The ratio of length of two pipes is
[DCE 2005]
Options:
A) 1 : 2
B) 4 : 1
C) 8 : 3
D) 3 : 8
Show Answer
Answer:
Correct Answer: A
Solution:
In first overtone of organ pipe open at one end, end, $ n _{c}=\frac{3v}{4l _{c}} $ …..(i) Third harmonic or second overtone of organ pipe open at both end, $ n _{0}=\frac{3v}{2l _{0}} $ …..(ii) given $ n _{c}=n _{o} $
$ \Rightarrow \frac{3v}{4l _{c}}=\frac{3v _{0}}{2l _{0}}\Rightarrow \frac{l _{c}}{l _{o}}=\frac{1}{2}.
$
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