Question

A standing wave is formed by the interference of two travelling waves, each of which has an amplitude $A=\pi cm$, angular wave number $k=\left(\pi /2\right)$ per centimetre. Calculate the distance between two successive antinodes(in cm).

Answer 1

For a standing wave of form $y=Asin\left(kx\right)cos\left(\omega t\right)$

$k=\frac{2\pi }{\lambda }$

where $\lambda$ is the wavelength of incident wave.

Thus here $\frac{2\pi }{\lambda }=\frac{\pi }{2}$

$⟹\lambda =4cm$

Distance between successive antinodes formed from a wave of wavelength $\lambda$ is $\frac{\lambda }{2}=2cm$