The second overtone of an open organ pipe has the same frequency as the first overtone of a closed pipe which is L meter long. The length of the open pipe will be

Step-by-step solution

Let the length of open organ pipe be L' . Frequency of second overtone of open organ pipe is given as, f 1 = 3 v 2 L ' , where v is speed of sound in air. Frequency of first overtone of closed pipe is given as, f 2 = 3 v 4 L . According to question, f 1 = f 2 3 v 2 L ' = 3 v 4 L ⇒ L ' = 2 L . Hence, length of open organ pipe must be twice the length of closed organ pipe.