A) \[\frac{2p}{2p-1}\]
B) \[\frac{p}{2p-1}\]
C) \[\frac{2p}{2p+1}\]
D) \[\frac{p}{2p+1}\]
Correct Answer: A
Solution :
As for the same length, if closed pipe has the frequency \[n,\] then open pipe will have the frequency \[2n.\] Now \[pth\] mode of vibration of open pipe will have frequency 2np and \[pth\] mode of vibration of closed pipe will have the frequency\[n\left( 2p-1 \right)\]. Hence ratio of frequency open pipe and closed pipe \[=\frac{2np}{n(2p-1)}=\frac{2p}{2p-1}\]
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