wave_mechanics organ_pipe_vibration_of_air_column Question 20
Question: A closed organ pipe and an open organ pipe are tuned to the same fundamental frequency. What is the ratio of lengths
[BHU 2003; Kerala 2005]
Options:
A) 1 : 2
B) 2 : 1
C) 2 : 3
D) 4 : 3
Show Answer
Answer:
Correct Answer: A
Solution:
Let $ l _{1} $ and $ l _{2} $ be the length’s of closed and open pipes respectively.
(Neglecting end correction) $ l _{1}=\frac{{\lambda _{1}}}{4}\Rightarrow {\lambda _{1}}=4l _{1} $ and $ l _{2}=\frac{{\lambda _{2}}}{2}\Rightarrow {\lambda _{2}}=2l _{2} $ Given $ n _{1}=n _{2} $ so $ \frac{v}{{\lambda _{1}}}=\frac{v}{{\lambda _{2}}}\Rightarrow \frac{v}{4l _{1}}=\frac{v}{2l _{2}}=\frac{l _{1}}{l _{2}}=\frac{1}{2} $
BETA
