A wave representing by the equation `y = a cos(kx - omegat)` is suerposed with another wave to form a stationary wave such that point `x = 0` is a node. The equation for the other wave is

Options

A. `y=a cos (kx-omega t)`
B. `y=a sin(kx-omega t)`
C. `y=-a sin(kx-omega t)`
D. `y=-a cos (kx-omega t)`

Answer

d

Explanation

When two similar waves propagating in opposite
directions superpose on each other, a new type of wave
is obtained which appears stationary in the medium.
Therefore, this wave is called stationary wave.
The equationn of given wave is `y= a cos (kx - omega t)`
The othe possible wave having opposite direction is
`y= -a cos (kx + omega t)`
Therefore, equation of stationary wave is
`y_(s)=y+y'=a cos (kx-omegat)-a cos (kx+omegat)`
`=2 a sin kx cdot sin omegat` At x=0 `y-(s)=2a sin ) cdot sin omegat = 0`
Therefore, a node is formed at `x=0`
`therefore` Hence, the other possible wave equation is
`y=1a cos (kx+omegat)`