Q: An open pipe resonates to a frequency f_{1} and a closed pipe resonates to a frequency f_{2}. If they are joined together to form a longer tube, then it will resonate to a frequency of (neglect end corrections)

(a) $ \displaystyle \frac{f_1 f_2}{2f_2 + f_1} $

(b) $ \displaystyle \frac{f_1 f_2}{f_2 + 2f_1} $

(c) $\displaystyle \frac{2 f_1 f_2}{f_2 + f_1} $

(d) $ \displaystyle \frac{f_1 + 2f_2}{f_1 f_2} $

Ans: (a)