The displacement $y$ of a wave travelling in the $x-$ direction is given by $y = {10^{ - 4}}\sin \left( {600t - 2x+\frac{\pi }{3}} \right)$ metre, where $x$ is expressed in metres and $t$ in seconds. The speed of the wave in $ms^{-1}$, is

Two vibrating strings of the same material but lengths $L$ and $2L$ have radii $2r$ and $r$ respectively. They are stretched under the same tension . Both the strings vibrate in their fundamental modes, the one of length $L$ with frequency $f_1$ and the other with frequency $f_2$. The ratio $\frac{f_1}{f_2}$ is given by

A train is moving towards a stationary observer (at $t = 0$) with constant velocity of $20\ m/s$ and after sometime it crosses the observer. Which of the following curve best represents the frequency received by observer $f$ as a function of time ?

A transverse wave is described by the equation $y = {y_0}\,\sin \,2\pi \,\left[ {ft - \frac{x}{\lambda }} \right]$ . The maximum particle velocity is equal to four times the wave velocity if

A train approaching a railway plateform with a speed of  $20\,\,m\,s^{-1}$ starts blowing the whistle speed of sound in air is $340\,\,ms^{-1}.$ If frequency of the emitted sound from the whistle is  $640\,\,Hz,$  the frequency of sound as heard by person standing on the platform is .... $Hz$

Two waves represented by

$y_1 = 10\,sin\,(2000\,\pi t + 2x)$

and ${y_2} = 10{\mkern 1mu} \,sin\,{\mkern 1mu} \left( {2000{\mkern 1mu} \pi t + 2x + \frac{\pi }{2}} \right)$ are superposed at any point at a particular instant. The resultant amplitude is ..... $unit$