A wave y=a (ω t-k x) on a string meets with another wave producing...

Equation of a wave $y_{1}=a \sin (\omega t-k x)$....(i) Let equations of another wave may be, $y_{2}=a \sin (\omega t+k x)$....(ii) $y_{3}=-a \sin (\omega t+k x) \quad \ldots.$ (iii) If Eq. (i) propagate with Eq. (ii), we get $\mathrm{y}=2 \mathrm{a} \cos \mathrm{kx} \sin \omega \mathrm{t}$ If Eq. (i), propagate with Eq. (iii), we get $y=-2 a \sin k x \cos \omega t$ At $x=0, y=0,$ wave produce node So, Eq.(iii) is the equation of unknown wave