Explanation

(c) Equation of given wave is
$y = a\cos(kx - \omega t)\ \ \ldots..(i)$
Let equation of other wave be
y=-a cos (kx+ωt) ………..(ii)
And y=a cos (kx+ωt) ………(iii)
If Eq. (i) propagates with Eq. (ii), then from the principle of superposition, we have
Eq.(i)+Eq.(ii)
∴ y=a cos (kx-ωt)-a cos (kx+ωt)
Y= a [cos (kx-ωt)-a cos (kx+ωt)]
Using
$\cos{A - \cos B} = 2\sin{\frac{A + B}{2}.\sin\frac{B - A}{2}},$
We get
Y=2a sin kx sin ωt ……………(iv)
Similarly when Eqs. (i) propagates with Eq. (iii), we get
Y=2a cos kx cos ωt
After putting x=0 ,in Eq.(iv) and (v),weget
Y=o and y=2a cos ωt
Hence Eq. (ii) is an equation of unknown wave.