Two closed organ pipes of length $100 \,cm$ and $101 \,cm$ produce $16$ beats in $20 \,s$. When each pipe is sounded in its fundamental mode,calculate the velocity of sound in $m/s$.

An empty vessel is partially filled with water. What happens to the frequency of vibration of the air column in the vessel?

In a pipe closed at one end,an air column is vibrating in its second overtone. The column has

An organ pipe filled with a gas at $27^{\circ}C$ resonates at $400\,Hz$ in its fundamental mode. If it is filled with the same gas at $90^{\circ}C$,the resonance frequency at the same mode will be $...........\,Hz$.

$A$ closed organ pipe and an open organ pipe of the same length produce $2$ beats per second when they are set into vibrations together in their fundamental mode. The length of the open pipe is now halved and that of the closed pipe is doubled. The number of beats produced per second will be:

$A$ closed organ pipe of length $l$ is sounded together with another closed organ pipe of length $l + x$ $(x << l)$,both in their fundamental mode. If $v$ is the speed of sound,the beat frequency heard is: