A pipe open at both ends has a fundamental frequency $f$ in air. The pipe is now dipped vertically in a water drum to half of its length. The fundamental frequency of the air column is now equal to:

The displacement of a travelling wave $$y=C \sin \frac{2 \pi}{\lambda}$$ (at $$-x$$) where $$t$$ is time, $$x$$ is distance and $$\lambda$$ is the wavelength, all in S.I. units. Then the frequency of the wave is

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