Equation of a plane progressive wave is given by $y = 0.6\, \sin 2\pi \left( {t - \frac{x}{2}} \right)$.On reflection from a denser medium its amplitude becomes $2/3$ of the amplitude of the  incident wave. The equation of the reflected wave is :-

A whistle revolves in a circle with an angular speed of $20\, rad/s$ using a string of length $50\, cm$. If the frequency of sound from the whistle is $385\, Hz$, then what is the minimum frequency heard by an observer, which is far away from the centre in the same plane  ..... $Hz$ (speed of sound is $340\, m/s$)

The equation of a stationary wave is $Y = 10\,\sin \,\frac{{\pi x}}{4}\,\cos \,20\,\pi t$. The distance between two consecutive nodes in metres is

A wave travelling along the $x-$ axis is described by the equation $y\ (x, t )\ =\ 0.005\ cos\ (\alpha x - \beta t )$ . If the wavelength and the time period of the wave in $0.08\ m$ and $2.0\ s$ respectively then $\alpha $ and $\beta $ in appropriate units are

Two open organ pipes of fundamental frequencies $n_1$ and $n_2$ are joined in series.  The fundamental frequency of the new pipe so obtained will be

A string of mass $M$ and length $L$ hangs freely from a fixed point. The velocity of transverse wave along the string at a distance $'x'$ from the free end will be