Question

The amplitude of a wave disturbance propagating in the positive x-direction is given by y = 1/(1 + $x^2$) at time t = 0 and y = 1/[1+ $(x-1{)}^2$] at t = 2 seconds where x and y are in metres. The shape of the wave disturbance does not change during the propagation. The velocity of the wave is

• A. 2.5 m/s
• B. 0.25 m/s
• C. 0.5 m/s
• D. 5 m/s

Answer 1

The correct option is C 0.5 m/s

here$,$

$y=1/(1+x^2)$ at $t=0sec$

$y=1/[1+(x-1{)}^2]$ at $t=2sec$

according to mathematics,[play with graph], if $f\left(x\right)=f(x-1),$ it means shape of graph is same just change the position. graph shift right direction by $1$ unit$.$

Here it is clear that the shape of wave doesn't change. also wave move in $2$sec , $1$m in positive $x$ direction

so$,$ wave moves $1m$ in $2sec.$

so$,$ velocity of wave $=$ displacement of wave $/$ time taken

$=1m/2sec=0.5m/sec$

So$,$ velocity of wave $=0.5m/s$

Hence,

option $\left(C\right)$ is correct answer.