An open pipe40 cm long a closed pipe 31 cm long , both having same diameter , are producing their first overtone , and these are in unison. Determine the end correction of these pipes.

An open pipe40 cm long a closed pipe 31 cm long , both having same dia

1.	An open pipe40 cm long a closed pipe 31 cm long , both having same diameter , are producing their first overtone , and these are in unison. Determine the end correction of these pipes.
Answer» Solution :Let `v` be the VELOCITY of sound and `f` be the frequency of the NOTE. Thus , the wavelength of sound produced is `lambda = (v)/(f)` The wavelength of first overtone of OPEN pipe is ` lambda_(1) = L + 2 e = 40 + 2E` `(v)/(f) = 40 + 2e``(:. lambda_(1)= lambda)` The wavelength of first overtone of closed pipe is `(3)/(4) lambda_(1) = l + e = 31 + e` `(3)/(4) ((v)/(f)) = 31 + e``( :. lambda_(1) = lambda)` By eliminating `v//f` from the above two equations , we get `(3)/(4) ( 40 + 2 e) = 31 + e` `rArr e = 2 cm`