The frequency of a fundamental note of an open organ pipe of length l_c is given by

\(f_c=\frac v{4l_c}\) ------- (i)

And the frequency of a fundamental note of an open organ pipe of length l₀ is given by 

\(f_0=\frac v{2l_0}\) ------- (ii)

Dividing equation (i) by equation (ii) we get,

\(\frac{f_c}{f_0}=\frac{l_0}{2l_c}\)

By the question, \(f_0=f_c,\frac{l_0}{l_c}=2,l_0=2l_c\). Hence, length of open pipe is double of closed pipe for the same fundamental frequency.