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

A closed organ pipe of length $L$ and an open organ pipe contain gases of densities ${\rho }_1$ and ${\rho }_2$ respectively. The compressibility of gases are equal in both the pipes. Both the pipes are vibrating in their first overtone with same frequency. The length of the open pipe is $\frac{x}{3}L\sqrt{\frac{{\rho }_1}{{\rho }_2}}$, where $x$ is _______.  

(Round off to the Nearest Integer)

How are stationary waves formed in closed pipes? Explain various modes of vibrations and obtain relations for their frequencies.

A closed organ pipe $70 \mathrm{cm}$ long is sounded. If the velocity of sound is $331 \mathrm{m} {\sec }^{-1}$, what is the fundamental frequency of vibrations of the air column?

A tuning fork is used to set up a wave in a pipe of length $L$ closed at one end (see figure).

Then,