A standing wave `xi= a sin kx. Cos omegat ` is maintained in a homogeneous rod with cross `-` sectional area `S` and density `rho`. Find the total mechanical energy confined between the sections corresponding to the adjacent displacement nodes.

A standing wave is maintained in a homogeneous string of cross-sectional area s and density rho . It is formed by the superposition of two waves travelling in opposite directions given by the equation y_1 = a sin (omega t - kx) " and " y_2 = 2a sin (omeg t + kx) . The total mechanical energy confined between the sections corresponding to the adjacent antinodes is

A standing wave is maintained in a homogeneous string of corss-sectional area 'S' and density phe . It is formed by the superposition of two waves travelling in opposite directions given by the equation y_(1)=asin(omegat=kx)andy_(2)=2asin(omegat+kx) . The total mechanical energy confined between the sections corresponding to the abjacent antinodes is:

A standing wave is maintained in a homogeneous string of cross - sectional area a and density p . It is formed at y\he superpositions given of two waves travelling in opposite directions given by the equations

A longitudinal standing wave xi a cos kx. Cos omega t is maintained in a homogeneous medium of density rho . Find the expressions for the space density of (a) potential energy w_(p)(x,t), (b) kinetic energy w_(k)(x,t), Plot the space density distribution of the total energy w in the space between the displacement nodes at the moments t=0 and t=T//4 , where T is oscillation period.

A longitudinal standing wave y = a cos kx cos omega t is maintained in a homogeneious medium of density rho . Here omega is the angular speed and k , the wave number and a is the amplitude of the standing wave . This standing wave exists all over a given region of space. If a graph E ( = E_(p) + E_(k)) versus t , i.e., total space energy density verus time were drawn at the instants of time t = 0 and t = T//4 , between two successive nodes separated by distance lambda//2 which of the following graphs correctly shows the total energy (E) distribution at the two instants.