The $3^{\text{rd}}$ overtone of a closed organ pipe is in unison with the $3^{\text{rd}}$ overtone of an open pipe. The ratio of the length of the closed pipe to the length of the open pipe is:

When an open pipe is closed from one end, the third overtone of the closed pipe is higher in frequency by $150 \,Hz$ than the second overtone of the open pipe. The fundamental frequency of the open pipe will be: (in $\,Hz$)

For air at room temperature, the atmospheric pressure is $1.0 \times 10^{5} \text{ Nm}^{-2}$ and the density of air is $1.2 \text{ kgm}^{-3}$. For a tube of length $1.0 \text{ m}$, closed at one end, the lowest frequency generated is $84 \text{ Hz}$. The value of $\gamma$ (ratio of two specific heats) for air is:

For sound waves, if the number of nodes for the $5^{th}$ harmonic of an open-ended pipe is $n$ and that for the $9^{th}$ harmonic of the same pipe with one of its ends closed is $m$, the ratio $\frac{n}{m}$ is :

The harmonics which are present in a pipe open at one end are

For a certain organ pipe,the first three resonance frequencies are in the ratio of $1:3:5$ respectively. If the frequency of the fifth harmonic is $405 \, Hz$ and the speed of sound in air is $324 \, ms^{-1}$,the length of the organ pipe is $.......... m$.