An organ pipe $P_1$ closed at one end vibrating in its first overtone and another pipe $P_2$ open at both ends vibrating in its third overtone are in resonance with a given tuning fork. The ratio of lengths of $P_1$ and $P_2$ is

In a resonance tube,the first resonance with a tuning fork occurs at $16 \ cm$ and the second at $49 \ cm$. If the velocity of sound is $330 \ m/s$,the frequency of the tuning fork is: (in $Hz$)

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

If $l_1$ and $l_2$ are the lengths of the air column for the first and second resonance when a tuning fork of frequency $n$ is sounded on a resonance tube,then the distance of the displacement antinode from the top end of the resonance tube is:

$A$ pipe open at both ends has a fundamental frequency '$f$' in air. The pipe is dipped in water, so that $\frac{2}{3}$ of its length is in water. Now, the fundamental frequency of the air column is:

An organ pipe $P_1$ closed at one end has a vibrating air column in its first overtone,and another pipe $P_2$ open at both ends has a vibrating air column in the third overtone. Both are in resonance with a given tuning fork. The ratio of the length of pipe $P_1$ to that of $P_2$ is