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 along the same direction
D. Both waves 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.