A uniform wire $$20 \mathrm{~m}$$ long and weighing $$50 \mathrm{~N}$$ hangs vertically. The speed of the wave at mid point of the wire is (acceleration due to gravity $$=\mathrm{g}=10 \mathrm{~ms}^{-2}$$ )

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