The transverse displacement of a string (clamped at its both ends) is given by $y(x,t) = 0.06$ $sin\, (2\pi x /3)\, cos\, (120\, \pi t)$. All the points on the string between two consecutive nodes vibrate with

Two trains $A$ and $B$ initially $120\, km$ apart, start moving towards each other on the same track with a velocity of $60\, km/hr$ each. At the moment of start $A$ blows a whistle, which reflects on $B$ and subsequently reflects from $A$ and so on. Take the velocity of sound waves in air $1200\, km/hr$. The distance travelled by sound waves before the trains crash will be (in $km$)

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

A transverse harmonic wave on a string is described by $y = 3\sin \left( {36t + 0.018x + \frac{\pi }{4}} \right)$ where $x$ and $y$ are in $cm$ and $t$ in $s$. The least distance between two successive crests in the wave is .... $m$

A transverse wave in a medium is described by the equation $y = A \sin^2 \,(\omega t -kx)$. The magnitude of the maximum velocity of particles in the medium will be equal to  that of the wave velocity, if the value of $A$ is ($\lambda$ = wavelngth of wave)

The phase difference between two points separated by $0.8 m$ in a wave of frequency $120 Hz$ is ${90^o}$. Then the velocity of wave will be ............ $\mathrm{m/s}$