Question

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

Answer 1

first overtone = 2nd harmonic so \[f _{2} = 2f _{1}\] for both systems... thus both also have the same fundamental frequency. For an open pipe, the length of the pipe is 1/2 wavelength, and for a closed pipe, length is 1/4 wavelength. Since we assume thier surroundings are at the same temperature (so that the speed of sound is the same for each system) then using\[f = v _{sound} /\lambda\] we have for the closed pipe\[f _{1}=v _{sound}/4L\] and for the open pipe\[f _{1}=v _{sound}/2L\] Setting them equal gives the length of the closed pipe has to be twice the length of the open pipe

Answer 2

thanx!