The wave function of a triangular wave pulse is defined by the relation below at time t=0 sec
`y={:(mx,"for "0 le x le a/2),(-m(x-a),fora/2lexlea),(0,every where else):}` The wave pulse is moving in the +x direction in a string having tension T and mass per unit length mu the total energy present with the wave pule is

Options

A. `(m^(2)Ta)/2`
B. `m^(2)Ta`
C. `(m^(2)Ta)/mu`
D. `(m^(2)Ta)/(2mu)`

Answer

B

Explanation

velocity of wave `v=sqrt(T/mu)`
velocity (v_(p))of particles are in y direction
`v_(p)=(dy)/(dt)=(dy)/((dx//v)) = v(dy)/(dx)=mv`
total kinetic energy `k=1/2m_(T)v^(2)=1/2muxx2av_(p)^(2) = 1/2mu2am^(2)v^(2)`
`=(m^(2)Ta)/mu`