$A$ sound wave is travelling with a frequency of $50 \,Hz$. The phase difference between two points in the path of the wave is $\frac{\pi}{3} \,rad$. The distance between those two points is (Velocity of sound in air $=330 \,m/s$) (in $m$)

$v_1$ and $v_2$ are the velocities of sound at the same temperature in two monoatomic gases of densities $\rho_1$ and $\rho_2$ respectively. If $\frac{\rho_1}{\rho_2} = \frac{1}{4}$,then the ratio of velocities $v_1$ and $v_2$ will be

$A$ source $S$ of frequency $f_0$ and an observer $O$,moving with speeds $v_1$ and $v_2$ respectively,are moving away from each other. When they are separated by a distance $a$ at $t = 0$,a pulse is emitted by the source. This pulse is received by $O$ at time $t_1$. Then $t_1$ is equal to:

$A$ sound wave passing through an ideal gas at $NTP$ produces a pressure change of $0.001 \ dyne/cm^2$ during adiabatic compression. The corresponding change in temperature $(\gamma = 1.5$ for the gas and atmospheric pressure is $1.013 \times 10^6 \ dyne/cm^2)$ is:

If at the same temperature and pressure,the densities of two diatomic gases are respectively $d_1$ and $d_2$,then the ratio of the velocities of sound in these gases will be

Velocity of sound in air:
$I.$ Increases with temperature
$II.$ Decreases with temperature
$III.$ Increases with pressure
$IV.$ Is independent of pressure
$V.$ Is independent of temperature
Choose the correct answer.