Consider the three waves $z_1$, $z_2$ and $z_3$ as $z_1 = A \sin (kx - \omega t)$, $z_2 = A \sin (kx +…
Consider the three waves $z_1$, $z_2$ and $z_3$ as $z_1 = A \sin (kx - \omega t)$, $z_2 = A \sin (kx + \omega t)$ and $z_3 = A \sin (ky - \omega t)$. Which of the following represents a standing wave?
$z_1 + z_2$
$z_2 + z_3$
$z_3 + z_1$
$z_1 + z_2 + z_3$
Solution
Wave, $z_1 = A \sin (kx - \omega t)$ is travelling towards positive $x$-direction.
Wave, $z_2 = A \sin (kx + \omega t)$ is travelling towards negative $x$-direction.
Wave, $z_3 = A \sin (ky - \omega t)$ is travelling towards positive $y$-direction.
Since, waves $z_1$ and $z_2$ are travelling along the same line in opposite directions, so they will produce a standing wave.