The frequency of the second overtone of an open pipe is equal to the frequency of the first overtone of a closed pipe. The ratio of the lengths of the open pipe to the closed pipe is

In a resonance tube experiment,the first resonance is obtained for $10\, cm$ of air column and the second for $32\, cm$. The end correction for this apparatus is ....$cm$

The lengths of two open organ pipes are $l$ and $(l + \Delta l)$ respectively. Neglecting end correction,the frequency of beats between them will be approximately (Here $v$ is the speed of sound).

In a resonance tube experiment,two consecutive resonances are observed when the lengths of the air columns are $16 \ cm$ and $49 \ cm$. If the frequency of the tuning fork used is $500 \ Hz$,the velocity of sound in air is $... \ ms^{-1}$.

Two pipes are each $50\,cm$ in length. One of them is closed at one end while the other is open at both ends. The speed of sound in air is $340\,ms^{-1}.$ The frequency at which both the pipes can resonate is

An organ pipe $P_1$ closed at one end vibrating in its first overtone and another pipe $P_2$ open at both ends vibrating in its third overtone are in resonance with a given tuning fork. The ratio of lengths of $P_1$ and $P_2$ is