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

Question

anonymous · Answer

You should mention that sound waves are generated in identical conditions i.e the speed of sound is same in the two experiments. 

In that case the ratio is 2v/2L1 :  3v/4L2 = 4L2 : 3L1 .

anonymous · Answer

In a closed pipe the fundamental is at L = 1/4 wavelength and the first overtone is at L = 3/4 wavelength (3rd harmonic). In an open pipe the fundamental is at L = 1/2 wavelength and the first overtone is L = 1 wavelength (2nd harmonic). So the length of the closed pipe is 3/4 the length of the open pipe.