$A$ steel rod $100 \,cm$ long is clamped at its middle. The fundamental frequency of longitudinal vibrations of the rod is given to be $2.53 \,kHz$. What is the speed of sound in steel in $km/s$?

An open and a closed organ pipe have the same length. The ratio of the $p^{th}$ mode of frequency of vibration of the two pipes is

An air column in a pipe,which is closed at one end,will be in resonance with a vibrating tuning fork of frequency $264 \,Hz$ for various lengths. Which one of the following lengths is not possible (in $\,cm$)? $(V=330 \,m/s)$

An open organ pipe of length $l$ is sounded together with another open organ pipe of length $(l+l_1)$ in their fundamental modes. Speed of sound in air is $V$. The beat frequency heard will be $(l_1 \ll l)$

$A$ closed organ pipe and an open organ pipe are filled with two different gases having the same bulk modulus but different densities $\rho_1$ and $\rho_2$ respectively. The frequency of the $9^{\text{th}}$ harmonic of the closed pipe is identical to the $4^{\text{th}}$ harmonic of the open pipe. If the length of the closed pipe is $10 \ cm$ and the density ratio of the gases is $\rho_1 : \rho_2 = 1 : 16$,then the length of the open pipe is:

The fundamental frequency of a closed organ pipe of length $20\; cm$ is equal to the second overtone of an organ pipe open at both the ends. The length of the organ pipe open at both the ends is ...... $cm$.