Sound waves of frequency $600 \,Hz$ fall normally on a perfectly reflecting wall. The shortest distance from the wall at which all particles will have maximum amplitude of vibration is (speed of sound $= 300 \,ms^{-1}$)

$n_{1}$ is the frequency of a pipe closed at one end and $n_{2}$ is the frequency of a pipe open at both ends. If both are joined end to end,find the fundamental frequency of the closed pipe so formed.

$A$ closed organ pipe of length $L$ and an open organ pipe of length $L'$ contain gases of densities $\rho_{1}$ and $\rho_{2}$ respectively. The compressibility of the gases is equal in both pipes. Both pipes are vibrating in their first overtone with the same frequency. The length of the open pipe is $L' = \frac{x}{3} L \sqrt{\frac{\rho_{1}}{\rho_{2}}}$,where $x$ is ......... . (Round off to the nearest integer)

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

$A$ tuning fork vibrating with a frequency of $512$ $Hz$ is kept close to the open end of a tube filled with water. The water level in the tube is gradually lowered. When the water level is $17$ $cm$ below the open end,maximum intensity of sound is heard. If the room temperature is $20^{\circ} C$,calculate:
$(a)$ Speed of sound in air at room temperature.
$(b)$ Speed of sound in air at $0^{\circ} C$.
$(c)$ If the water in the tube is replaced with mercury,will there be any difference in your observations?

An open and a closed organ pipe have the same length. The ratio of the $p^{th}$ mode of frequency of vibration of the two pipes is