A plane wave (y=a ( t-k x) ) propagates through a stretched string. The particle velocity versus (x ) graph at (t=0 ) is

Step-by-step solution

Plane wave is given as (y=a ( t-k x) ) at (t=0 ), ( aligned & y=a ( 0-k x) & =a (-k x) -a k x aligned ) Particle velocity, ( aligned v_ pa & = d y d t = d d t (-a k x) & =-a k k x=-a k 2 x [ k= 2 ] & =- 2 a 2 x (i) aligned ) From Eq. (i), When (x=0, v_ pa = -2 a 0= -2 a ) When (x= 4 , v_ pa = -2 a 2 =0 ) When (x= 2 , v_ pa = -2 a = 2 a ) When (x= 3 4 , v_ pa = -2 a ( - 2 )=0 ) When (x= , v_ pa = -2 a 2 = -2 a ) Hence, correct graph is