Question

A closed pipe and an open pipe have their first overtones identical in frequency. their lengths are in the ratio?

Answer 1

A closed pipe has nodes (zero amplitude) at both ends while a open pipe has maximum wave amplitude at the open end. Thus, the fundamental wave length of an open pipe is 1/4 the pipe length while, for the closed pipe, it is 1/2. (The fundamental frequency of the closed pipe is twice that of the open pipe of the same length.) If I interpret first overtone correctly, there would be one full wave length in a closed pipe and 3/4 wave lengths in an open pipe. Thus to have the same frequency, the open pipe would be 3/4 as long as the closed pipe.