A standing wave is represented by `y=2Asinkx cos omegat. ` If one of the component waves is `y_(1)=A sin (omega t-k x)`, what is the equation of the second component wave?

Explanation

As, `2sinA cosB=sin(A+B)+sin(A-B)`
`:. Y=2A sin k x cos omegat `
`=Asin (kx+omegat)+A sin(kx-omegat)`
According to superposition principle,
`y=y_(1)+y_(2),`
and `y_(1)=A sin (omegat -kx)`
`=-A sin(kx-omegat)`
`:. Y_(2)=y-y_(1)`
`=2Asin k x cos omega t +A sin (kx-omegat )`
`=A sin (kx+omegat) +2A sin (kx-omegat)`
`=A sin (kx+omegat)-2Asin(omegat-kx)`