The displacement due to a wave moving in the positive x-direction is given by y=1(1+x2) at time t = 0 and by y=1[1+(x−1)2] at t = 2 seconds, where x and y are in metres. The velocity of the wave in m/s is

In a wave equation, x and t must be related in the form (x−v t).We rewrite the given equations y=11+(x−v t)2For t = 0, this becomes y=1(1+x2), as givenFor t = 2, this becomes y=1[1+(x−2v)2]=1[1+(x−1)2]⇒2v=1 or v=0.5m/s.