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An open pipe 40 cm long and a closed pip...

An open pipe 40 cm long and a closed pipe 31 cm long, both having same dimeter, are producing their first overtone, and these are in unison. The end correction of these pipes is :

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Verified by Experts

The correct Answer is:
2
`lambda=(upsilon)/(f)`
For open pipe :
`lambda_(1)=l+2e=40+2e`
`implies(upsilon)/(f)=40+2e`
For closed pipe : `lambda_(2)=l+e`
`implies (3)/(4) lambda_(1)=31+e[ because lambda_(c)=(3)/(4)lambda_(0)]`
`implies (3)/(4)((upsilon)/(f))=31+e..........(ii)`
From (i) and (ii)
`(3)/(4)(40+2e)=31+e`
`implies e=2 cm`
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