An open pipe 40 cm long and 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. (in cm)

Let  $v$ be the velocity of sound and  $v$ be the frequency of the note. Thus the wavelength of sound produced is  $\lambda =\frac{v}{v}$
The wavelength of first overtone of organ pipe is
${\lambda }_1=l+2e=40+2e\Rightarrow \frac{v}{v}=40+2e(\therefore {\lambda }_1=\lambda )$
The wavelength of first overtone  of close pipe is
$\frac{3}{4}{\lambda }_1=l+e=3l+e\Rightarrow \frac{3}{4}\left(\frac{v}{v}\right)=3l+e(\therefore {\lambda }_1=\lambda )$
By eliminating $\frac{v}{v}$  from the above two equations, we get
$\frac{3}{4}(40+2e)=3l+e\Rightarrow 120+6e=3l+e\Rightarrow e=2cm$