Two uniform strings ' $A$ ' and ' $B$ ' made of steel are made to vibrate under same tension. If the first overtone of ' $A$ ' is equal to second overtone of ' B ' and radius of ' A ' is twice that of ' B '. Then the ratio of length of string ' $A$ ' to that of ' $B$ ' is

The pitch of whistle of an engine appears to drop by $30 \%$ of the original value when it passes a stationary observer. If speed of sound in air is $350 \mathrm{~m} / \mathrm{s}$, then the speed of engine in $\mathrm{m} / \mathrm{s}$ is

The equation of simple harmonic progressive wave is given by $y=A \sin (100 \pi t-4 x)$. The distance between two particles having a phase difference of $\left(\frac{\pi}{4}\right)^c$ is