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

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.

Options

A. There is no position at which resultant displacement will be zero at all times
B. there is no times at which resultant displacement will be zero everywhere
C. both waves travel along the same direction
D. Both wave travel in opposite directions.

Answer

D

Explanation

Resultant Displacement
`y'=y_(1)+y_(2)`
for y to be zero
`(2x-3t)^(2)=(2x-3t-6)^(2)`
on solving `(x-3/2 ) (t-1)=0`
Therefore
at `x=3/2`, resultant displacement is zero for all values of t.
According to equations both waves are travelling in opposite directions.