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.
The space density of the kinetic energy . `KE = E_(k) ( x, t)` at the point `(x, t)` is given by

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. The space density of the potential energy PE = E_(p)(x , t) at a point (x , t) in this space is

Standing waves

Standing waves

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.

Standing Waves

Standing Waves

Find out the equation of the standing waves for the following standing wave pattern.

Energy OF travelling & standing waves

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 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.