$A$ pipe open at both ends and a pipe closed at one end have the same length. The ratio of the frequencies of the air columns in their $p^{\text{th}}$ overtone respectively is

If the velocity of sound in air is $350 \ m/s$,then the fundamental frequency of an open organ pipe of length $50 \ cm$ will be ............... $Hz$.

An air column is of length $17 \ cm$. The ratio of frequencies of the $5^{\text{th}}$ overtone for an air column closed at one end to that open at both ends is (velocity of sound in air $= 340 \ ms^{-1}$).

The fundamental frequency of a closed pipe is equal to the frequency of the second harmonic of an open pipe. The ratio of their lengths is

$A$ tuning fork of frequency $480\, Hz$ is used in an experiment for measuring the speed of sound $(\nu)$ in air by the resonance tube method. Resonance is observed to occur at two successive lengths of the air column,$\ell_1 = 30\, cm$ and $\ell_2 = 70\, cm$. Then $\nu$ is equal to ..... $m/s$.

The third overtone of a closed pipe of length '$L_c$' has the same frequency as the third overtone of the open pipe of length '$L_0$'. Both the pipes have same diameters. The ratio $L_c : L_0$ is equal to