Wave Mechanics Question 1117
Question: An organ pipe $ P _{1} $ closed at one end vibrating in its first overtone and another pipe $ P _{2} $ open at both ends vibrating in its third overtone are in resonance with a given tuning fork. The ratio of lengths of $ P _{1} $ and $ P _{2} $ is
[EAMCET 1997; MH CET 1999; AFMC 2001]
Options:
A) 1 : 2
B) 1 : 3
C) 3 : 8
D) 3 : 4
Show Answer
Answer:
Correct Answer: C
Solution:
First overtone of closed organ pipe $ n _{1}=\frac{3v}{4l _{1}} $ Third overtone of open organ pipe $ n _{2}=\frac{4v}{2L _{2}} $
$ n _{1}=n _{2} $ (Given) $ \Rightarrow $ $ \frac{3v}{4L _{1}}=\frac{4v}{2L _{2}}\Rightarrow $
$ \frac{L _{1}}{L _{2}}=\frac{3}{8} $
BETA
