The $$4^{\text {th }}$$ overtone of a closed organ pipe is same as that of $$3^{\text {rd }}$$ overtone of an open pipe. The ratio of the length of the closed pipe to the length of the open pipe is :

The ratio of frequencies of fundamental harmonic produced by an open pipe to that of closed pipe having the same length is

An organ pipe filled with a gas at 27$$^\circ$$C resonates at 400 Hz in its fundamental mode. If it is filled with the same gas at 90$$^\circ$$C, the resonance frequency at the same mode will be

If the initial tension on a stretched string is doubled, then the ratio of the initial and final speeds of a transverse wave along the string is