In an organ pipe closed at one end,the sum of the frequencies of the first three overtones is $3930 \ Hz$. The frequency of the fundamental mode of the organ pipe is: (in $Hz$)

$A$ cylindrical tube $(L = 120 \, cm)$ is resonant with a tuning fork of frequency $330 \, Hz$. If it is being filled with water,then to get resonance again,the minimum length of the water column is ...... $cm$ $(v_{air} = 330 \, m/s)$.

$A$ closed organ pipe of length $L_1$ and an open organ pipe contain diatomic gases of densities $\rho_1$ and $\rho_2$ respectively. The compressibilities of the gases are same in both pipes,which are vibrating in their first overtone with the same frequency. The length of the open organ pipe is (Neglect end correction).

$A$ metre-long tube open at one end,with a movable piston at the other end,shows resonance with a fixed frequency source (a tuning fork of frequency $340\; Hz$) when the tube length is $25.5\; cm$ or $79.3\; cm$. Estimate the speed of sound (in $m/s$) in air at the temperature of the experiment. The edge effects may be neglected.

$A$ student determines the velocity of sound with the help of a closed organ pipe. If the observed length for the fundamental frequency is $24.7 \, cm$,the length for the third harmonic will be .... $cm$.

$A$ tuning fork of frequency $340 \, Hz$ is vibrated just above a cylindrical tube of length $120 \, cm$. Water is slowly poured into the tube. If the speed of sound is $340 \, m/s$,then the minimum height of water required for resonance is .... $cm$.