A travelling wave represented by
`y=Asin (omegat-kx)`
is superimposed on another wave represented by
`y=Asin(omegat+kx).` The resultant is

Options

A. A standing wave having nodes at
`x=(n+(1)/(2))(lambda)/(2),n=0,1,2`
B. A wave travellling along `+x` direction
C. A wave travelling along `-x` direction
D. A standing wave having nodes at
`x=(nlambda)/(2),n=0,1,2,`

Answer

A

Explanation

`y=A sin (omegat-kx)+Asin(omegat=kx)`
or `y=2Asinomegat cos kx`
It represents a standing wave.
In standing wave, there will be nodes at locations where`y=0.` It will be so if `cos kx=0`.
or `kx=(2n+1)(pi)/(2)`where`n=0,1,2,3,`
or `(2pi)/(lambda)x=(2n+1)(pi)/(2)`
or `x=(2n+1)(lambda)/(4),n=0,1,2,3`
`=(n+(1)/(2))(lambda)/(2),=0,1,2,......`