Two wave function in a medium along x direction are given by
`y_(1)=1/(2+(2x-3t)^(2))m`, `y_(2)=-1/(2+(2x+3t-6)^(2))m`
Where x is in meters and t is in seconds

Options

A. There is no position at which resultant displacement will be zero at all times
B. There is no time at which resultant displacement will be zero everywhere.
C. Both waves travel in same directions.
D. Both waves travel in oppoisite directions.

Answer

D

Explanation

Resultant displacement
`y=y_(1)+y_(2)`
for y to be zero
y=0
`(2x-3t)^(2)=(2x+3t-6)^(2)`
on solving `(x-3/2)(t-1) =0`
Therefore,
at `x=3/2`, resultant displacement is zero all values of t.