A car sounding a horn of frequency $$1000 \mathrm{~Hz}$$ passes a stationary observer. The ratio of frequencies of the horn noted by the observer before and after passing the car is $$11: 9$$. If the speed of sound is '$$v$$', the speed of the car is

A transverse wave $$\mathrm{Y}=2 \sin (0.01 \mathrm{x}+30 \mathrm{t})$$ moves on a stretched string from one end to another end in 0.5 second. If $$x$$ and $$y$$ are in $$\mathrm{cm}$$ and $$t$$ in second, then the length of the string is

The fundamental frequency of air column in pipe 'A' closed at one end is in unison with second overtone of an air column in pipe 'B' open at both ends. The ratio of length of air column in pipe '$$\mathrm{A}$$' to that of air column in pipe '$$\mathrm{B}$$' is

The equation of wave is $$Y=6 \sin$$ $$\left(12 \pi t-0.02 \pi x+\frac{\pi}{3}\right)$$ where '$$x$$' is in $$m$$ and '$$t$$' in $$\mathrm{s}$$. The velocity of the wave is