$A$ cylindrical tube open at both ends has a fundamental frequency $f$ in air. The tube is dipped vertically in water so that $60 \%$ of the tube is in water. Then the fundamental frequency of the air column is

In a resonance tube,the first and second resonances are obtained at depths $22.7 \,cm$ and $70.2 \,cm$ respectively. The third resonance will be obtained at a depth of: (in $\,cm$)

Two open organ pipes of fundamental frequencies $n_1$ and $n_2$ are joined in series. The fundamental frequency of the new pipe so obtained will be

Four open organ pipes of different lengths and different gases at the same temperature are shown in the figure. Let $f_A$,$f_B$,$f_C$,and $f_D$ be their fundamental frequencies. Then: [Take $\gamma_{CO_2} = 7/5$]

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

An air column in a tube of length $L = 50 \ cm$,closed at one end,is vibrating in its fifth harmonic. The phase difference between a particle at the open end and a particle at $42 \ cm$ from the open end is: (in $^{\circ}$)