Wave Mechanics Question 619

Question: 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) $ $ z _{3}=A\sin (ky-\omega t) $ Which of the following represents a standing wave?

Options:

A) $ z _{1}+z _{2} $

B) $ z _{2}+z _{3} $

C) $ z _{3}+z _{1} $

D) $ z _{1}+z _{2}+z _{3} $

Show Answer

Answer:

Correct Answer: A

Solution:

[a] Standing waves are produced when two waves propagate in opposite direction. As $ z _{1} $ & $ z _{2} $ are propagating in $ +ve,x-ax $ is $ -ve,x-axis $ so, $ z _{1}+z _{2} $ will represent a standing wave.