$A$ 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 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)

The first overtone in a closed pipe has a frequency:

The stationary wave $y = 2a \sin kx \cos \omega t$ in a closed organ pipe is the result of the superposition of $y = a \sin (\omega t - kx)$ and

$A$ uniform narrow $1.95 \, m$ long pipe is open at both ends. It resonates at two successive harmonics of frequency $275 \, Hz$ and $330 \, Hz$. The speed of sound in the tube is ...... $m/s$.

$A$ closed pipe is suddenly opened and changed to an open pipe of the same length. The fundamental frequency of the resulting open pipe is less than that of the $3^{rd}$ harmonic of the earlier closed pipe by $55 \,Hz$. Then, the value of the fundamental frequency of the closed pipe is: (in $\,Hz$)