A wave propagates in a string in the positive x-direction with velocity v. The shape of the string at `t=t_0` is given by
`f(x,t_0)=A sin ((x^2)/(a^2))`. Then the wave equation at any instant t is given by

A wave pulse is travelling on a string with a speed v towards the positive X-axis. The shape of the string at t = 0 is given by g(x) = A sin(x /a) , where A and a are constants. (a) What are the dimensions of A and a ? (b) Write the equation of the wave for a general time 1, if the wave speed is v.

A wave pulse is travelling on a string at 2m//s along positive x-directrion. Displacement y of the particle at x = 0 at any time t is given by y = (2)/(t^(2) + 1) Find Shape of the pulse at t = 0 and t = 1s.

A wave is propagating along x-axis. The displacement of particles of the medium in z-direction at t=0 is given by : z= exp[-(x+2)^(2)] where 'x' is in meter. At t=1s, the same wave disturbance is given by z=exp[-(x-2)^(2)] . Then the wave propagation velocity is :-

A sinusoidal wave having wavelength of 6 m propagates along positive x direction on a string. The displacement (y) of a particle at x = 2 m varies with time (t) as shown in the graph (a) Write the equation of the wave (b) Draw y versus x graph for the wave at t = 0

A sinusoidal wave y=a sin ((2pi)/lambda x-omegat) is travelling on a stretched string. An observer is travelling along positive x direction with a velocity equal to that of the wave. Find the angle that the velocity of a particle on the string at x=lambda/6 makes with -x direction as seen by the observer at time t=0 .

A wave is propagating in positive x- direction. A time t=0 its snapshot is taken as shown. If the wave equation is y=A sin(omegat-Kx+phi) , then phi is