Question

Consider the three waves, $z_1,z_2$ and $z_3$ as $z_1=\text{A sin}(kx-\omega t),z_2=\text{A sin}(kx+\omega t)$ and $z_3=\text{A sin}(ky-\omega t)$. Which of the following represents a standing wave?

• A. $z_1+z_2$
• B. $z_2+z_3$
• C. $z_3+z_1$
• D. $z_2+2z_3$

Answer 1

The correct option is A $z_1+z_2$

Stationary waves are formed by the superposition of two identical waves traveling in opposite directions along the same axis.
$z_1=\text{A sin}(kx-\omega t)$ $\to$ travel along $+x$ axis.
$z_2=\text{A sin}(kx+\omega t)$ $\to$ travel along $-x$ axis.
$z_3=\text{A sin}(ky-\omega t)$ $\to$ travel along $+y$ axis.
So, according to definition, $z_1+z_2$ represents the standing wave.