The first resonance length of a resonance tube is $40\, cm$ and the second resonance length is $122\, cm$. The third resonance length of the tube will be... $cm$

The air column in an organ pipe closed at one end is made to vibrate so that there are $2$ nodes and $2$ antinodes each. The mode of vibration is called:

$A$ tuning fork is used to produce resonance in a glass tube. The length of the air column in this tube can be adjusted by a variable piston. At room temperature of $27\,^{\circ}C$,two successive resonances are produced at $20\,cm$ and $73\,cm$ of column length. If the frequency of the tuning fork is $320\,Hz$,the velocity of sound in air at $27\,^{\circ}C$ is .... $m/s$.

The frequency of the third overtone of a pipe of length $L_c$,closed at one end,is the same as the frequency of the sixth overtone of a pipe of length $L_o$,open at both ends. Then the ratio $L_c : L_o$ is

$A$ pipe $P_{C}$ closed at one end and a pipe $P_{O}$ open at both ends are vibrating in their second overtone. They are in resonance with a given tuning fork. The ratio of the length of pipe $P_{C}$ to $P_{O}$ is (Neglect end correction):

If the speed of sound in air is $330 \, m/s$,find the number of tones (harmonics) present in an open organ pipe of length $1 \, m$ whose frequency is $\leq 1000 \, Hz$.