$A$ student determines the velocity of sound with the help of a closed organ pipe. If the observed length for the fundamental frequency is $24.7 \, cm$,the length for the third harmonic will be .... $cm$.

Two closed pipes have the same fundamental frequency. One is filled with oxygen and the other with hydrogen at the same temperature. The ratio of their lengths respectively is

The frequency of a vibrating air column in a pipe,open at both ends,is $f_1$. When $\frac{3}{4}$ of its length is immersed in water,the frequency of the vibrating air column is $f_2$. The value of $\frac{f_1}{f_2}$ is

Two closed organ pipes having lengths $20\,cm$ and $20.5\,cm$ produce $5\,beats/sec$. Determine the frequency of both organ pipes.

The first overtone frequency of a closed organ pipe is equal to the first overtone frequency of an open organ pipe. Further,the $n^{th}$ harmonic of the closed organ pipe is also equal to the $m^{th}$ harmonic of the open pipe,where $n$ and $m$ are:

Give the equation for the normal modes of vibration for a closed pipe.