The temperature at which the speed of sound in air becomes double of its value at $0^oC$ is ...... $K$.

$A$ 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 $m$)

One Mach number is equal to

Assume that the displacement $(s)$ of air is proportional to the pressure difference $(\Delta p)$ created by a sound wave. Displacement $(s)$ further depends on the speed of sound $(v)$,density of air $(\rho)$,and the frequency $(f)$. If $\Delta p \approx 10 \, Pa$,$v \approx 300 \, m/s$,$\rho \approx 1 \, kg/m^3$,and $f \approx 1000 \, Hz$,then $s$ will be of the order of (take multiplicative constant to be $1$).

The velocity of sound is $v_s$ in air. If the density of air is increased to $4$ times,then the new velocity of sound will be

$A$ string is stretched so that its length is increased by $\frac{1}{\eta }$ of its original length. The ratio of the fundamental frequency of transverse vibration to that of the fundamental frequency of longitudinal vibration will be