Question

Find the three smallest values of x corresponding to antinodes.

Answer 1

The interfering waves have form $y_1=Asin(kx-\omega t)$ and $y_2=Asin(kx+\omega t)$

Thus the resultant wave has displacement $y=y_1+y_2$

$=2Asin\left(kx\right)cos\left(\omega t\right)$

When antinodes are formed, displacement is maximum at those points.

Thus $kx=\frac{\pi }{2},\frac{3\pi }{2},\frac{5\pi }{2}........$

$⟹\pi x=\frac{\pi }{2},\frac{3\pi }{2},\frac{5\pi }{2}.....$

$⟹x=0.5cm,1.5cm,2.5cm$