The fundamental frequency of a closed pipe is $220 \ Hz$. If $\frac{1}{4}$ of the pipe is filled with water,the frequency of the first overtone of the pipe now is ..... $Hz$.

$A$ closed pipe of length $10 \, cm$ has its fundamental frequency half that of the second overtone of an open pipe. The length of the open pipe is ......... $cm$.

If $v$ is the speed of sound in air,then what is the shortest length of a closed pipe that resonates at a frequency $n$?

Two open organ pipes give $4$ beats/sec when sounded together in their fundamental modes. If the lengths of the pipes are $100 \ cm$ and $102.5 \ cm$ respectively,then the velocity of sound is ..... $m/s$.

$A$ pipe open at both ends has a length of $1 \,m$. The air column in the pipe cannot resonate for which of the following frequencies (in $\,Hz$)? (Neglect end correction, speed of sound in air $= 340 \,m/s$)

$A$ pipe open at both ends and a pipe closed at one end have the same length. The ratio of the frequencies of the air columns in their $p^{\text{th}}$ overtone respectively is