A passenger is sitting in a train which is moving fast. The engine of the train blows a whistle of frequency '$$n$$'. If the apparent frequency of sound heard by the passenger is '$$f$$' then

The equation of wave motion is $$Y=5 \sin (10 \pi t -0.02 \pi x+\pi / 3)$$ where $$x$$ is in metre and $$t$$ in second. The velocity of the wave is

End correction at open end for air column in a pipe of length '$$l$$' is '$$e$$'. For its second overtone of an open pipe, the wavelength of the wave is

A tuning fork gives 3 beats with $$50 \mathrm{~cm}$$ length of sonometer wire. If the length of the wire is shortened by $$1 \mathrm{~cm}$$, the number of beats is still the same. The frequency of the fork is