$A$ 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 ..... $m/s$.

For a certain organ pipe,three successive resonance frequencies are observed at $425 \, Hz$,$595 \, Hz$,and $765 \, Hz$ respectively. If the speed of sound in air is $340 \, m/s$,then the length of the pipe is ..... $m$.

$A$ closed organ pipe and an open organ pipe have their first overtones identical in frequency. Their lengths are in the ratio:

An organ pipe $P_1$, closed at one end and containing a gas of density $\rho_1$ is vibrating in its first harmonic. Another organ pipe $P_2$, open at both ends and containing a gas of density $\rho_2$ is vibrating in its third harmonic. Both the pipes are in resonance with a given tuning fork. If the compressibility of gases is equal in both pipes, the ratio of the lengths of $P_1$ and $P_2$ is (assume the given gases to be monoatomic)

$A$ student performed an experiment to measure the speed of sound in air using the resonance air-column method. Two resonances in the air-column were obtained by lowering the water level. The resonance with the shorter air-column is the first resonance and that with the longer air-column is the second resonance. Then,

When an air column in a pipe open at both ends vibrates such that four antinodes and three nodes are formed,then the corresponding mode of vibration is